Here is the full list of all 45 Dwarf Tower achievements.
Put a Dwarf dwelling to the 10th floor of your tower
Have 10 crystals at the same time
Build the lowest dungeon room possible
Reach round 25
Miss three times in a row using a Ray or Disturmance spell
Build 7 libraries at the same time
Build a tower 10 blocks high
Save a room by moving it (the old block is destroyed the same turn)
Equip Archmage with doors and armor
Remove water from a flooded room by digging earth under it
Hide your room that was visible to the enemy by moving it or using the Anti-Eye spell.
Put a crystal underground
Find the enemy Archmage room by using the Eye spell
Have 5 of your rooms burning at the same time
Have all your rooms destroyed except the archmage.
Gather 50 Mana
Make an enemy crystal explode from fire
Use doors to stop fire or water from spreading.
Ignite 5 enemy rooms at the same time
Win a match in under 5 rounds
Win your first battle
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.
Win 10 online matches in a row
Make 10 enemy blocks fall down at the same time
Have a fire put out with water
Win a match without using any Dwarves.
Win a match without using any spells
Build a tower 10 blocks wide
Win the game by using a Collapse spell
Pump water from the Archmage room
Dig out 15 blocks of earth
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
Destroy enemy Archmage with a spell reflector
Use 5 movers during one round
Use 5 lightning strikes in one attack
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