Play the first song in LOCAL endurance and last for ten minutes. You can not do online endurance for this - you will have to find a local boosting buddy and play together. There is a separate achievement for doing it online over Xbox Live.
Otherwise, it's pretty straight forward... just survive for ten minutes. For the first two or three minutes, it's insanely easy - just tap A or B in sync with the prompts, and then break as many blocks as you can (go for big combos and always try to hit the bombs). They'll start throwing in X and Y for a few minutes, then LT and RT (they'll RARELY throw in LB and RB), then up / down / left / right on the left stick. For the last minute, you'll also have to deal with combos (ie, LT+X).
Survive for ten minutes, and the achievement will unlock for both of you.