Here is the full list of all 15 Mouse Playhouse achievements.
Finish the tutorial
Finish level 1-5
Finish level 2-5
Finish level 3-5
Complete all of leve set 1's Star Scores
Complete all of level set 2's Star Scores
Complete all of level set 3's Star Scores
Complete all Star Scores
Hit the bullseye for the darts
Make a basket
Throw the rocket
Punch the clown 10 times
Get the mouse on top of 7 blocks
Get all the hats
Trap a meowbot