Here is the full list of all 19 Tiles achievements.
Publish a level
Clear 100 user created levels
Clear 50 user created levels
Clear 25 user created levels
Clear 10 user created levels
Win a game in multiplayer mode
Beat the goal times on all the local levels
Clear all the local levels
Start on level 1 and clear all 90 levels without going back to the menu
Beat 60 of the goal times on the local levels
Clear the 5th page of local levels
Clear the 4th page of local levels
Clear the 3rd page of local levels
Step on to an orange tile the moment it appears
Beat 30 of the goal times on the local levels
Fail to complete the same level 25 times in a row
Clear the 2nd page of local levels
Step off of a blue tile just as it falls away.
Clear the 1st page of local levels