What a Feeling

I have made a weak aura helper that makes it easier to do this, especialy if you are planing to fast spam it just for achievement.
https://wago.io/luxBzCtoV

While the oponent is performing his dance moves, click the icons you see on the center of the screen.
When its your turn to perform. spam the center button that appears and that will execute the sequence you inputed.

edit:
Weak aura updated for Dragonflight ui changes.

I know that I'm going to get a bunch of haters because of this comment, but this IS possible to do without addons! If you have trouble remembering, try saying the colors out loud as they occur. It might help with remembering them in the correct order. You do not have to wait a long time to get started with your turn, so it's not TOO long to remember.... but if it gets frustrating then you always know there appears to be an addon to help. You don't HAVE to use it, though.

And to clarify, you need to complete 10 perfect dance games on each level to get the toy. You will end up doing all of the dancing achievements on your way to get it!

Although it looks like there's a Global Cooldown on the dance move buttons, one can simply input the key sequence disregarding that visual representation of a GCD and it'll still qualify as correct -- this minigame - as is at this point - isn't about matching timing but purely about entering the identical order of dance moves. Also, once the bout is won, one can press the 'Leave Game' action button to quickly end the scenario (rather than sitting through the crowd's applaud bit each time!)