To rob the bank quickly, we're going to use mnemonics.

First, we assign a letter to each of the dancer's poses. This allows us to memorize the pose positions using as little data as possible.

To compress things even further, we want to pair adjacent letters so that they can combine into a single syllable. In this arrangement, starting with the top pose on the right and going clockwise, the letters are M, T, K, R, F, S, L, and Y. We combine these into pairs, so MT, KR, FS, LY. I would say these out loud as "mit", "kir" (pronounced like "cur"), "fis" ("fist" without the 't'), and "ly" ("lie"). I prefer inserting a short 'i' vowel sound to keep things simple and consistent (except for pairs ending in Y, which always rhyme with "lie"), but you can substitute other vowel sounds if it helps you remember them better. Just don't spend too much time thinking up words on the spot.

Now, we want to minimize the number of peeks we make before beginning the puzzle. You can click on a pose cover to force it to open up a bit faster, rather than wait for them to open slowly one-by-one. Because we can miss up to four times before the trap blows up, we don't have to peek at all of them. The minimum number of peeks to guarantee a successful disarm (assuming no mistakes during memorization) is three, so if you want to ensure success, peek at the first three poses. This will give you one syllable and one extra letter. Whenever the dancer shows a pose that you haven't seen before, start peeking at other poses and adding them to your mnemonic. Repeat aloud every syllable you have memorized to keep them firmly in your brain.

Watch this video to see the technique in action (timestamp 1:13:29):

Of course, you could also do fewer than three peeks if you want to shave a few seconds, but this introduces the possibility of failure. I wrote a quick simulation to calculate the chances of failure for each number of peeks, and these are the results:

0-peek: 28% chance of success, average of 3.46 incorrect guesses 1-peek: 54% chance of success, average of 3.32 incorrect guesses 2-peek: 83% chance of success, average of 3.06 incorrect guesses 3-peek: 100% chance of success, average of 2.55 incorrect guesses

On average, each pre-puzzle peek will net cost you about a second, but each incorrect guess costs you about 2.5 seconds, so the variance is pretty high. Unless you're grinding for super-fast RNG, I recommend using three peeks every time.