Thanks! I had been using “letsencrypt” because I was following the instructions provided for Debian/wheezy rather than Debian/other. It turns out that running letsencrypt with sudo got rid of the “Illegal instruction” result, but still didn’t seem to work (or at least generated no output).
When I switched to the Debian/other instructions, which use certbot-auto, it popped up their nice ncurses interface and seems to work just fine. Thanks again!
The plugins provide both authenticator and installer mechanisms, so it can make sense to use apache together with certonly -- the apache plugin can be used for authentication purposes without using the corresponding installer.
Okay, I figured out why I got an “Illegal instruction” failure. It was because the installed version of “libaugeas0” did not support ARMv6 (I am running a Raspberry Pi Model B+). I could solve this by following the instructions over here: https://github.com/certbot/certbot/issues/2673.
Everything working fine now and I have installed a Letsencrypt certificate on my Pi :-).