Well, thats quite a big list.
I'm aware theres a lot of things to update, but i'm afraid to break something when i do it, since i was not responsible for this droplet initial setup.
Heres the list:
apt/xenial-updates 1.2.35 amd64 [upgradable from: 1.2.32ubuntu0.2]
apt-transport-https/xenial-updates 1.2.35 amd64 [upgradable from: 1.2.32ubuntu0.2]
apt-utils/xenial-updates 1.2.35 amd64 [upgradable from: 1.2.32ubuntu0.2]
bind9-host/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
bsdutils/xenial-updates 1:2.27.1-6ubuntu3.10 amd64 [upgradable from: 1:2.27.1-6ubuntu3.4]
btrfs-tools/xenial-updates 4.4-1ubuntu1.1 amd64 [upgradable from: 4.4-1ubuntu1]
cloud-guest-utils/xenial-updates 0.27-0ubuntu25.2 all [upgradable from: 0.27-0ubuntu25.1]
cloud-initramfs-copymods/xenial-updates 0.27ubuntu1.6 all [upgradable from: 0.27ubuntu1.5]
cloud-initramfs-dyn-netconf/xenial-updates 0.27ubuntu1.6 all [upgradable from: 0.27ubuntu1.5]
console-setup/xenial-updates 1.108ubuntu15.5 all [upgradable from: 1.108ubuntu15.3]
console-setup-linux/xenial-updates 1.108ubuntu15.5 all [upgradable from: 1.108ubuntu15.3]
curl/xenial-updates,xenial-security 7.47.0-1ubuntu2.19 amd64 [upgradable from: 7.47.0-1ubuntu2.18]
debconf/xenial-updates 1.5.58ubuntu2 all [upgradable from: 1.5.58ubuntu1]
debconf-i18n/xenial-updates 1.5.58ubuntu2 all [upgradable from: 1.5.58ubuntu1]
distro-info-data/xenial-updates,xenial-security 0.28ubuntu0.18 all [upgradable from: 0.28ubuntu0.16]
dmidecode/xenial-updates 3.0-2ubuntu0.2 amd64 [upgradable from: 3.0-2ubuntu0.1]
dnsmasq-base/xenial-updates,xenial-security 2.75-1ubuntu0.16.04.10 amd64 [upgradable from: 2.75-1ubuntu0.16.04.7]
dnsutils/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
do-agent/main 3.12.0 amd64 [upgradable from: 3.9.0]
dpkg/xenial-updates 1.18.4ubuntu1.7 amd64 [upgradable from: 1.18.4ubuntu1.4]
dpkg-dev/xenial-updates 1.18.4ubuntu1.7 all [upgradable from: 1.18.4ubuntu1.4]
friendly-recovery/xenial-updates 0.2.31ubuntu2.1 all [upgradable from: 0.2.31ubuntu1]
git/xenial-updates,xenial-security 1:2.7.4-0ubuntu1.10 amd64 [upgradable from: 1:2.7.4-0ubuntu1.9]
git-man/xenial-updates,xenial-security 1:2.7.4-0ubuntu1.10 all [upgradable from: 1:2.7.4-0ubuntu1.9]
grub-common/xenial-updates 2.02~beta2-36ubuntu3.32 amd64 [upgradable from: 2.02~beta2-36ubuntu3.27]
grub-efi-amd64/xenial-updates 2.04-1ubuntu44.1.2 amd64 [upgradable from: 2.02~beta2-36ubuntu3.27]
grub-efi-amd64-bin/xenial-updates 2.04-1ubuntu44.1.2 amd64 [upgradable from: 2.02~beta2-36ubuntu3.27]
grub-efi-amd64-signed/xenial-updates 1.167~16.04.6+2.04-1ubuntu44.1.2 amd64 [upgradable from: 1.66.27+2.02~beta2-36ubuntu3.27]
grub-legacy-ec2/xenial-updates 21.1-19-gbad84ad4-0ubuntu1~16.04.2 all [upgradable from: 18.2-4-g05926e48-0ubuntu1~16.04.2]
grub-pc-bin/xenial-updates 2.02~beta2-36ubuntu3.32 amd64 [upgradable from: 2.02~beta2-36ubuntu3.27]
grub2-common/xenial-updates 2.02~beta2-36ubuntu3.32 amd64 [upgradable from: 2.02~beta2-36ubuntu3.27]
guile-2.0-libs/xenial-updates 2.0.11+1-10ubuntu0.1 amd64 [upgradable from: 2.0.11+1-10]
ifupdown/xenial-updates 0.8.10ubuntu1.4 amd64 [upgradable from: 0.8.10ubuntu1.3]
initramfs-tools/xenial-updates 0.122ubuntu8.17 all [upgradable from: 0.122ubuntu8.14]
initramfs-tools-bin/xenial-updates 0.122ubuntu8.17 amd64 [upgradable from: 0.122ubuntu8.14]
initramfs-tools-core/xenial-updates 0.122ubuntu8.17 all [upgradable from: 0.122ubuntu8.14]
iproute2/xenial-updates 4.3.0-1ubuntu3.16.04.5 amd64 [upgradable from: 4.3.0-1ubuntu3.16.04.3]
keyboard-configuration/xenial-updates 1.108ubuntu15.5 all [upgradable from: 1.108ubuntu15.3]
kmod/xenial-updates 22-1ubuntu5.2 amd64 [upgradable from: 22-1ubuntu5]
libapt-inst2.0/xenial-updates 1.2.35 amd64 [upgradable from: 1.2.32ubuntu0.2]
libapt-pkg5.0/xenial-updates 1.2.35 amd64 [upgradable from: 1.2.32ubuntu0.2]
libbind9-140/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
libblkid1/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
libc-bin/xenial-updates,xenial-security 2.23-0ubuntu11.3 amd64 [upgradable from: 2.23-0ubuntu11.2]
libc-dev-bin/xenial-updates,xenial-security 2.23-0ubuntu11.3 amd64 [upgradable from: 2.23-0ubuntu11.2]
libc6/xenial-updates,xenial-security 2.23-0ubuntu11.3 amd64 [upgradable from: 2.23-0ubuntu11.2]
libc6-dev/xenial-updates,xenial-security 2.23-0ubuntu11.3 amd64 [upgradable from: 2.23-0ubuntu11.2]
libcurl3/xenial-updates,xenial-security 7.47.0-1ubuntu2.19 amd64 [upgradable from: 7.47.0-1ubuntu2.18]
libcurl3-gnutls/xenial-updates,xenial-security 7.47.0-1ubuntu2.19 amd64 [upgradable from: 7.47.0-1ubuntu2.18]
libdns-export162/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
libdns162/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
libdpkg-perl/xenial-updates 1.18.4ubuntu1.7 all [upgradable from: 1.18.4ubuntu1.4]
libdrm-common/xenial-updates 2.4.91-2~16.04.1 all [upgradable from: 2.4.83-1~16.04.1]
libdrm2/xenial-updates 2.4.91-2~16.04.1 amd64 [upgradable from: 2.4.83-1~16.04.1]
libfdisk1/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
libglib2.0-0/xenial-updates,xenial-security 2.48.2-0ubuntu4.8 amd64 [upgradable from: 2.48.2-0ubuntu4.6]
libglib2.0-data/xenial-updates,xenial-security 2.48.2-0ubuntu4.8 all [upgradable from: 2.48.2-0ubuntu4.6]
libhogweed4/xenial-updates,xenial-security 3.2-1ubuntu0.16.04.2 amd64 [upgradable from: 3.2-1ubuntu0.16.04.1]
libisc-export160/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
libisc160/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
libisccc140/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
libisccfg140/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
libjs-sphinxdoc/xenial-updates 1.3.6-2ubuntu1.2 all [upgradable from: 1.3.6-2ubuntu1.1]
libjs-underscore/xenial-updates,xenial-security 1.7.0~dfsg-1ubuntu1.1 all [upgradable from: 1.7.0~dfsg-1ubuntu1]
libkmod2/xenial-updates 22-1ubuntu5.2 amd64 [upgradable from: 22-1ubuntu5]
libldap-2.4-2/xenial-updates,xenial-security 2.4.42+dfsg-2ubuntu3.13 amd64 [upgradable from: 2.4.42+dfsg-2ubuntu3.12]
liblwres141/xenial-updates,xenial-security 1:9.10.3.dfsg.P4-8ubuntu1.19 amd64 [upgradable from: 1:9.10.3.dfsg.P4-8ubuntu1.17]
liblxc1/xenial-updates 2.0.11-0ubuntu1~16.04.3 amd64 [upgradable from: 2.0.8-0ubuntu1~16.04.2]
libmount1/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
libnettle6/xenial-updates,xenial-security 3.2-1ubuntu0.16.04.2 amd64 [upgradable from: 3.2-1ubuntu0.16.04.1]
libpam-modules/xenial-updates 1.1.8-3.2ubuntu2.3 amd64 [upgradable from: 1.1.8-3.2ubuntu2.1]
libpam-modules-bin/xenial-updates 1.1.8-3.2ubuntu2.3 amd64 [upgradable from: 1.1.8-3.2ubuntu2.1]
libpam-runtime/xenial-updates 1.1.8-3.2ubuntu2.3 all [upgradable from: 1.1.8-3.2ubuntu2.1]
libpam-systemd/xenial-updates 229-4ubuntu21.31 amd64 [upgradable from: 229-4ubuntu21.27]
libpam0g/xenial-updates 1.1.8-3.2ubuntu2.3 amd64 [upgradable from: 1.1.8-3.2ubuntu2.1]
libpci3/xenial-updates 1:3.3.1-1.1ubuntu1.3 amd64 [upgradable from: 1:3.3.1-1.1ubuntu1.2]
libplymouth4/xenial-updates 0.9.2-3ubuntu13.5 amd64 [upgradable from: 0.9.2-3ubuntu13.4]
libprocps4/xenial-updates 2:3.3.10-4ubuntu2.5 amd64 [upgradable from: 2:3.3.10-4ubuntu2.4]
libpython2.7/xenial-updates,xenial-security 2.7.12-1ubuntu0~16.04.18 amd64 [upgradable from: 2.7.12-1ubuntu0~16.04.13]
libpython2.7-minimal/xenial-updates,xenial-security 2.7.12-1ubuntu0~16.04.18 amd64 [upgradable from: 2.7.12-1ubuntu0~16.04.13]
libpython2.7-stdlib/xenial-updates,xenial-security 2.7.12-1ubuntu0~16.04.18 amd64 [upgradable from: 2.7.12-1ubuntu0~16.04.13]
libpython3.5/xenial-updates,xenial-security 3.5.2-2ubuntu0~16.04.13 amd64 [upgradable from: 3.5.2-2ubuntu0~16.04.12]
libpython3.5-minimal/xenial-updates,xenial-security 3.5.2-2ubuntu0~16.04.13 amd64 [upgradable from: 3.5.2-2ubuntu0~16.04.12]
libpython3.5-stdlib/xenial-updates,xenial-security 3.5.2-2ubuntu0~16.04.13 amd64 [upgradable from: 3.5.2-2ubuntu0~16.04.12]
libseccomp2/xenial-updates 2.5.1-1ubuntu1~16.04.1 amd64 [upgradable from: 2.4.3-1ubuntu3.16.04.3]
libslang2/xenial-updates 2.3.0-2ubuntu1.1 amd64 [upgradable from: 2.3.0-2ubuntu1]
libsmartcols1/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
libssl1.0.0/xenial-updates,xenial-security 1.0.2g-1ubuntu4.20 amd64 [upgradable from: 1.0.2g-1ubuntu4.18]
libsystemd0/xenial-updates 229-4ubuntu21.31 amd64 [upgradable from: 229-4ubuntu21.27]
libtiff5/xenial-updates,xenial-security 4.0.6-1ubuntu0.8 amd64 [upgradable from: 4.0.6-1ubuntu0.7]
libudev1/xenial-updates 229-4ubuntu21.31 amd64 [upgradable from: 229-4ubuntu21.27]
libuuid1/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
linux-headers-generic/xenial-updates,xenial-security 4.4.0.210.216 amd64 [upgradable from: 4.4.0.201.207]
linux-headers-virtual/xenial-updates,xenial-security 4.4.0.210.216 amd64 [upgradable from: 4.4.0.201.207]
linux-image-virtual/xenial-updates,xenial-security 4.4.0.210.216 amd64 [upgradable from: 4.4.0.201.207]
linux-libc-dev/xenial-updates,xenial-security 4.4.0-210.242 amd64 [upgradable from: 4.4.0-201.233]
linux-virtual/xenial-updates,xenial-security 4.4.0.210.216 amd64 [upgradable from: 4.4.0.201.207]
locales/xenial-updates,xenial-security 2.23-0ubuntu11.3 all [upgradable from: 2.23-0ubuntu11.2]
login/xenial-updates 1:4.2-3.1ubuntu5.4 amd64 [upgradable from: 1:4.2-3.1ubuntu5.3]
lshw/xenial-updates 02.17-1.1ubuntu3.6 amd64 [upgradable from: 02.17-1.1ubuntu3.5]
lxc-common/xenial-updates 2.0.11-0ubuntu1~16.04.3 amd64 [upgradable from: 2.0.8-0ubuntu1~16.04.2]
mokutil/xenial-updates,xenial-security 0.3.0+1538710437.fb6250f-0ubuntu2~16.04.1 amd64 [upgradable from: 0.3.0-0ubuntu3]
mount/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
multiarch-support/xenial-updates,xenial-security 2.23-0ubuntu11.3 amd64 [upgradable from: 2.23-0ubuntu11.2]
open-iscsi/xenial-updates 2.0.873+git0.3b4b4500-14ubuntu3.7 amd64 [upgradable from: 2.0.873+git0.3b4b4500-14ubuntu3.4]
open-vm-tools/xenial-updates 2:10.2.0-3~ubuntu0.16.04.1 amd64 [upgradable from: 2:10.0.7-3227872-5ubuntu1~16.04.2]
openssh-client/xenial-updates 1:7.2p2-4ubuntu2.10 amd64 [upgradable from: 1:7.2p2-4ubuntu2.8]
openssh-server/xenial-updates 1:7.2p2-4ubuntu2.10 amd64 [upgradable from: 1:7.2p2-4ubuntu2.8]
openssh-sftp-server/xenial-updates 1:7.2p2-4ubuntu2.10 amd64 [upgradable from: 1:7.2p2-4ubuntu2.8]
overlayroot/xenial-updates 0.27ubuntu1.6 all [upgradable from: 0.27ubuntu1.5]
passwd/xenial-updates 1:4.2-3.1ubuntu5.4 amd64 [upgradable from: 1:4.2-3.1ubuntu5.3]
pciutils/xenial-updates 1:3.3.1-1.1ubuntu1.3 amd64 [upgradable from: 1:3.3.1-1.1ubuntu1.2]
plymouth/xenial-updates 0.9.2-3ubuntu13.5 amd64 [upgradable from: 0.9.2-3ubuntu13.4]
plymouth-theme-ubuntu-text/xenial-updates 0.9.2-3ubuntu13.5 amd64 [upgradable from: 0.9.2-3ubuntu13.4]
pollinate/xenial-updates 4.33-0ubuntu1~16.04.1 all [upgradable from: 4.25-0ubuntu1~16.04.1]
postfix/xenial-updates 3.1.0-3ubuntu0.4 amd64 [upgradable from: 3.1.0-3ubuntu0.3]
procps/xenial-updates 2:3.3.10-4ubuntu2.5 amd64 [upgradable from: 2:3.3.10-4ubuntu2.4]
psmisc/xenial-updates 22.21-2.1ubuntu0.1 amd64 [upgradable from: 22.21-2.1build1]
python-apt-common/xenial-updates 1.1.0~beta1ubuntu0.16.04.12 all [upgradable from: 1.1.0~beta1ubuntu0.16.04.11]
python2.7/xenial-updates,xenial-security 2.7.12-1ubuntu0~16.04.18 amd64 [upgradable from: 2.7.12-1ubuntu0~16.04.13]
python2.7-minimal/xenial-updates,xenial-security 2.7.12-1ubuntu0~16.04.18 amd64 [upgradable from: 2.7.12-1ubuntu0~16.04.13]
python3-apt/xenial-updates 1.1.0~beta1ubuntu0.16.04.12 amd64 [upgradable from: 1.1.0~beta1ubuntu0.16.04.11]
python3-distupgrade/xenial-updates 1:16.04.32 all [upgradable from: 1:16.04.25]
python3-josepy/xenial 1.1.0-2+ubuntu16.04.1+certbot+1 all [upgradable from: 1.0.1-1+ubuntu16.04.1+certbot+7]
python3-update-manager/xenial-updates 1:16.04.17 all [upgradable from: 1:16.04.13]
python3.5/xenial-updates,xenial-security 3.5.2-2ubuntu0~16.04.13 amd64 [upgradable from: 3.5.2-2ubuntu0~16.04.12]
python3.5-minimal/xenial-updates,xenial-security 3.5.2-2ubuntu0~16.04.13 amd64 [upgradable from: 3.5.2-2ubuntu0~16.04.12]
resolvconf/xenial-updates 1.78ubuntu7 all [upgradable from: 1.78ubuntu6]
rsyslog/xenial-updates 8.16.0-1ubuntu3.1 amd64 [upgradable from: 8.16.0-1ubuntu3]
sbsigntool/xenial-updates,xenial-security 0.6-0ubuntu10.2 amd64 [upgradable from: 0.6-0ubuntu10.1]
screen/xenial-updates,xenial-security 4.3.1-2ubuntu0.1 amd64 [upgradable from: 4.3.1-2build1]
secureboot-db/xenial-updates 1.4~ubuntu0.16.04.1 amd64 [upgradable from: 1.1]
shared-mime-info/xenial-updates 1.5-2ubuntu0.2 amd64 [upgradable from: 1.5-2ubuntu0.1]
shim/xenial-updates 15.4-0ubuntu7 amd64 [upgradable from: 13-0ubuntu2]
shim-signed/xenial-updates 1.33.1~16.04.10+15.4-0ubuntu7 amd64 [upgradable from: 1.33.1~16.04.1+13-0ubuntu2]
sosreport/xenial-updates 3.9.1-1ubuntu0.16.04.2 amd64 [upgradable from: 3.5-1~ubuntu16.04.2]
squashfs-tools/xenial-updates 1:4.3-3ubuntu2.16.04.3 amd64 [upgradable from: 1:4.3-3ubuntu2.16.04.1]
systemd/xenial-updates 229-4ubuntu21.31 amd64 [upgradable from: 229-4ubuntu21.27]
systemd-sysv/xenial-updates 229-4ubuntu21.31 amd64 [upgradable from: 229-4ubuntu21.27]
ubuntu-keyring/xenial-updates 2012.05.19.1 all [upgradable from: 2012.05.19]
ubuntu-minimal/xenial-updates 1.361.6 amd64 [upgradable from: 1.361.1]
ubuntu-release-upgrader-core/xenial-updates 1:16.04.32 all [upgradable from: 1:16.04.25]
ubuntu-standard/xenial-updates 1.361.6 amd64 [upgradable from: 1.361.1]
udev/xenial-updates 229-4ubuntu21.31 amd64 [upgradable from: 229-4ubuntu21.27]
uidmap/xenial-updates 1:4.2-3.1ubuntu5.4 amd64 [upgradable from: 1:4.2-3.1ubuntu5.3]
unattended-upgrades/xenial-updates 1.1ubuntu1.18.04.7~16.04.7 all [upgradable from: 0.90ubuntu0.10]
update-manager-core/xenial-updates 1:16.04.17 all [upgradable from: 1:16.04.13]
update-notifier-common/xenial-updates 3.168.15 all [upgradable from: 3.168.8]
ureadahead/xenial-updates 0.100.0-19.1 amd64 [upgradable from: 0.100.0-19]
util-linux/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
uuid-runtime/xenial-updates 2.27.1-6ubuntu3.10 amd64 [upgradable from: 2.27.1-6ubuntu3.4]
vlan/xenial-updates 1.9-3.2ubuntu1.16.04.5 amd64 [upgradable from: 1.9-3.2ubuntu1.16.04.4]
Can you point any evidence responsible for curl not working with the longer chain on that list?
If so, how can i update without breaking everything up? Any tips?