Succinct phrase for "work well under pressure"?

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.)

According to vocabulary.com, aplomb is defined as composure under pressure/stress. They give the following definition

Aplomb is the ultimate test for cool: grace under pressure. Use aplomb to show great restraint under even the most trying circumstances. In retail, it's always a good idea to handle the angry customers with aplomb.

Also, according to WordNet 3.1, aplomb means

Assuredness, cool, poise, sang-froid (great coolness and composure under strain) "keep your cool"

I'm not sure it's the best choice for your CV (it's not very common), but it's a nice word, notwithstanding.

This is the most overlooked word you’re describing: “equanimity,” which means steadiness of mind under stress.

collected, level-headed, established, persevering, tenacious, unflinching, unshakable; you could also explore some synonyms of these words.

Personally, I think "pressure performer" doesn't sound right, while multi-tasking means something else entirely - the ability to focus on several tasks at once, with no reference to pressure.

An idiomatic expression would be to keep a cool head

To maintain a calm demeanor and think clearly in a difficult, stressful, or troubling situation

[The Free Dictionary]

Personal Point of View

If you are wondering if using idioms in resumes is informal, I have used idioms and phrases while creating my own resume and being in IT, I do review quite a few resumes. I prefer people who can include figurative sense in their write-ups. The ability to use idiomatic expressions shows your fluency and command of the language.