Hi @Yohasakoura,
Can you please give examples of what you tried and what error messages you got?
Most of the documentation that you'll find is about setting up TLS support for a web server (HTTPS), but it looks like what you're interested is TLS support for a mail server (STARTTLS or SMTPS). This is a less common (though still quite important) use case, so there may be less documentation focused on it.
In the particular error that you posted here, it looks to me like this is actually an outbound error where your server is trying to deliver e-mail from your site to Hotmail, rather than in inbound error where Hotmail is trying to connect to you to deliver mail. Do you agree with that interpretation? If that's so, resolving this particular error does not require you to get a certificate or to configure the certificate in your mail server because a TLS certificate in the STARTTLS security model is only presented by the server (the destination/recipient of the e-mail), not the client (the origin/sender of the e-mail). The reason for this particular error would then be something else about your configuration—not the lack of a certificate on your end.
However, we would still be happy to try to help you get a certificate set up on your mail server even if that's not the underlying reason for the error that you're receiving.