I found this achievement a bit tricky to unlock so here is my solution below.
In the video below I show you how to get 2 of the 3 badges to unlock the Team Player Achievement. **SKIP TO 0:50 in video, I restarted and forgot to edit that out*
Badges needed to unlock Team Player:
Hanger On - basically select one of the Tetribots on the right hand side of the screen while on the menu screen, the one you want on your team being the first selected. Then pick the remaining two tetribots, these will be the ones you will play against.
Tag Team Champions - this one is tricky but the best way I have figured out to do it is to use a second controller/guest on your team and build up your blocks with no gaps on each side of the board and save the 2 middle shared columns for the combo. Make sure to have any piece other than a blue "long" piece in your hold spot when you decide to go for the 3 combo. See video around the 2:00 mark.
Back 2 Back - same concept as above but build up your blocks with no gaps and save one column to drop 2 blue long pieces back to back. See video around 4:25 mark.