Here is the full list of all 45 Dwarf Tower achievements.
Win a match in under 5 rounds
Win your first battle
Have 5 of your rooms burning at the same time
Ignite 5 enemy rooms at the same time
Survive and extinguish 5 burning rooms during one turn
Sink the enemy archmage room separated from the dungeon with doors.
Win an online match by using bombs only.
Use the levitronus room to hold your tower with no ground blocks left.
Win the game with a succcessful use of the Rat spell.
Use doors to stop fire or water from spreading.
Find the enemy Archmage room by using the Eye spell
Make an enemy crystal explode from fire
Hide your room that was visible to the enemy by moving it or using the Anti-Eye spell.
Put a crystal underground
Remove water from a flooded room by digging earth under it
Win 10 online matches in a row
Make 10 enemy blocks fall down at the same time
Have all your rooms destroyed except the archmage.
Have a fire put out with water
Win a match without using any Dwarves.
Win a match without using any spells
Build the lowest dungeon room possible
Build a tower 10 blocks high
Build a tower 10 blocks wide
Win the game by using a Collapse spell
Have 10 crystals at the same time
Pump water from the Archmage room
Dig out 15 blocks of earth
Put a Dwarf dwelling to the 10th floor of your tower
Miss three times in a row using a Ray or Disturmance spell
Put 3 roofs on your tower
Damage 5 rooms using one Earthquake spell
Save 5 rooms at the same time with the help of the Deratiser improvement
Build 7 libraries at the same time
Gather 50 Mana
Save a room by moving it (the old block is destroyed the same turn)
Destroy enemy Archmage with a spell reflector
Use 5 movers during one round
Reach round 25
Use 5 lightning strikes in one attack
Equip Archmage with doors and armor
Save the tower from falling thanks to an extra connection to ground.
Use all possible spells in one attack.
Have an underground-only construction by turn 15.
Build 25 rooms