to remember to speak slowly, breathe deeply,

[keannu]

This is kind of ambiguous, is it 1 or 2 or can it be either depending on your interpretation?

1.to remember to (speak slowly, breathe deeply, try to enjoy themselves, and smile.)
2.(to remember to speak slowly), (breathe deeply), (try to enjoy themselves), and (smile).

rp105)Except for those who speak in public as part of their job, few people have any experience or training in public speaking....Even when they have had time to prepare, the majority of inexperienced speakers will still feel very nervous...But when they finally take the mike and start the speech they have prepared, the terrible feelings of nervousness usually disappear. All they have to do is to remember to speak slowly, breathe deeply, try to enjoy themselves, and smile.

[5jj]

It could be either. It doesn't really make a difference.

[Kotfor]

I have a feeling that "to" is optional here.

All they have to do is (to) remember

[Tdol]

I can't see a huge difference- if they do these things, then they have remembered to do them. I doubt that many native speakers would worry about the brackets to be honest.