There's an in-game timer whenever you go into one of the two game-modes.
Either let it run out by idling, or actually play the game. It's more efficient to idle because they make you watch a 7-8 minute cutscenes upon completion of either game mode which stops the timer. But I found this game somewhat entertaining, so if you so desire, you may decide to play it.
You will get achievements for
5 minutes
10 minutes
15 minutes
20 minutes
25 minutes
30 minutes
35 minutes
40 minutes
45 minutes
50 minutes
55 minutes
60 minutes
Enjoy!