As someone who has read a lot of resumes, works well under pressure works for me.
It is succinct and clear.
I would not know what you meant by "Pressure performer"; I would find that term in a resume irritating. My immediate picture when I first saw it in your question was of a dancer in a hyperbaric chamber.
A multitasker may or may not be able to work well under pressure; the ability to do several things at the same time is no guarantee that the person will not fall apart under pressure.
If you want to add something to the "works well under pressure", say "meets deadlines".
(You are right to agonize over your resume.)