Here is the full list of all 36 Palallel achievements.
Play with a player you already played with
Finish all non bonus levels of world 2
Play once on side A and on side B
Move 1000 in game units
Get hit by an object 25 times
Finish all non bonus levels of world 1
Discover World 1
Discover World 2
Discover World 3
Discover World 4
Discover World 5
Discover World 6
Discover World 7
Discover World 8
Finish all non bonus levels of world 3
Finish all non bonus levels of world 4
Finish all non bonus levels of world 5
Finish all non bonus levels of world 6
Finish all non bonus levels of world 7
Finish all non bonus levels of world 8
Finish all levels of world 1
Finish all levels of world 2
Finish all levels of world 3
Finish all levels of world 4
Finish all levels of world 5
Finish all levels of world 6
Finish all levels of world 7
Finish all levels of world 8
Open 50 doors using keys
Trade 100 objects with your pal
Ping 3 times in 1 second
Spam ready 3 times in 1 second
Spam a button 4 times in 1 second
Trade 3 objects in 8 seconds
Finish all non bonus levels
Finish the game at 100%