Here is the full list of all 85 Hexrogue achievements.
Reached Lv 2
Reached Lv 5
Reached Lv 10
Reached Lv 15
Reached Lv 20
Reached Lv 25
Surviving 12 Turns
Surviving 24 Turns
Surviving 36 Turns
Surviving 48 Turns
Surviving 60 Turns
Surviving 72 Turns
Surviving 84 Turns
Surviving 96 Turns
Surviving 108 Turns
Surviving 120 Turns
Acquired "Runner II"
Acquired "Kill Streak III"
Acquired "Combo II"
Acquired "Smash II"
Acquired "Area Repair"
Acquired "Building Master"
Acquired "Catapult"
Acquired "Farmers"
Acquired "Commander II"
Acquired "Spell: Fireball III"
Acquired "Spell: Protection II"
Acquired "Spell: Haste"
Acquired "Spell: Landmine III"
Built 1 Fortress III
Built 1 Plantation V
Built 1 Brick Workshop V
Built 1 Farm V
Built 1 Mine V
Built 1 Temple III
Built 1 Trading Port III
Total Attack Reached 16
Total Attack Reached 24
Total Attack Reached 40
Total Attack Reached 56
Total Attack Reached 72
Total Defense Reached 16
Total Defense Reached 24
Total Defense Reached 40
Total Defense Reached 56
Total Defense Reached 72
Built 1 Architecture
Built 6 Architecture
Built 12 Architecture
Built 24 Architecture
Crafted a +1 Equipment
Crafted a +2 Equipment
Acquired a Unique Bow
Acquired a Unique Hammer
Acquired a Unique Spear
Acquired a Unique Holy Sword
Acquired a Unique Robe
Acquired a Unique Coat
Acquired a Unique Black Belt
Acquired a Unique Sacred Armor
Acquired a Unique Gauntlets
Acquired a Unique Sacred Shield
Defeated 10 Monsters
Defeated 20 Monsters
Defeated 30 Monsters
Defeated 40 Monsters
Defeated 50 Monsters
Defeated 1 Golem I
Defeated 1 Bear I
Defeated 1 Necromancer I
Defeated 1 Goblin Lord I
Defeated 1 Golem II
Defeated 1 Bear II
Defeated 1 Necromancer II
Defeated 1 Goblin Lord II
Defeated 1 Golem III
Defeated 1 Bear III
Defeated 1 Necromancer III
Defeated 1 Goblin Lord III
Defeated 1 Dragon
Defeated or Repelled The Dragon with Fighter
Defeated or Repelled The Dragon with Builder
Defeated or Repelled The Dragon with Spell Caster
Beat The Game with All Classes
Acquired All Achievements