Here is the full list of all 43 BATTLE OF TILES EX trophies - there are 22 bronze, 18 silver, 2 gold and 1 platinum.
Buy an enemy tile
Get all trophies
Defeat king slime on the very easy difficulty level
Defeat king skeleton on the very easy difficulty level
Defeat king scorpion on the very easy difficulty level
Defeat dark king on the very easy difficulty level
Defeat dragon on the very easy difficulty level
Defeat king slime on the easy difficulty level
Defeat king skeleton on the easy difficulty level
Defeat king scorpion on the easy difficulty level
Defeat dark king on the easy difficulty level
Defeat dragon on the easy difficulty level
Defeat king slime on the normal difficulty level
Defeat king skeleton on the normal difficulty level
Defeat king scorpion on the normal difficulty level
Defeat dark king on the normal difficulty level
Defeat dragon on the normal difficulty level
Defeat king slime on the hard difficulty level
Defeat king skeleton on the hard difficulty level
Defeat king scorpion on the hard difficulty level
Defeat dark king on the hard difficulty level
Defeat dragon on the hard difficulty level
Defeat king slime on the very hard difficulty level
Defeat king skeleton on the very hard difficulty level
Defeat king scorpion on the very hard difficulty level
Defeat dark king on the very hard difficulty level
Defeat dragon on the very hard difficulty level
Clear round 2 on the very easy difficulty level
Clear round 3 on the very easy difficulty level
Clear round 4 on the very easy difficulty level
Clear round 2 on the easy difficulty level
Clear round 3 on the easy difficulty level
Clear round 2 on the normal difficulty level
One of your allied tiles become level 50
One of your allied tiles become level 100
One of your allied tiles become level 200
One of your allied tiles become level 300
One of your allied tiles become level 400
One of your allied tiles become level 500
Heal an allied tile
Buy tsuchinoko
Buy dark knight
Buy gargoyle