Here is the full list of all 37 The Last King's Archer achievements.
Die
Die 10 times
The King is Dead
Collect 500
Collect 5000
Collect 10000
Collect 30000
Collect 50000
Collect 70000
Complete All Archer's Upgrades
Complete All Fire Dragon's Upgrades
Complete All Thunder Dragon's Upgrades
Shoot 10 arrows
Shoot 100 arrows
Shoot 500 arrows
Shoot 1000 arrows
Shoot 10 Fire Arrows
Shoot 30 Fire Arrows
Shoot 50 Fire Arrows
Shoot 5 Thunder Arrows
Shoot 10 Thunder Arrows
Shoot 30 Thunder Arrows
Kill 10 Globins
Kill 100 Globins
Kill 300 Globins
Kill 500 Globins
Kill 10 Bigger Globin
Kill 50 Bigger Globin
Kill 10 Flying Creature
Kill 50 Flying Creature
Kill 100 Flying Creature
Kill 50 Mushroom Creature
Protect The King
Complete Globin's Party Mode
Complete Flying Attack Mode
Complete Mushroom Infestation Mode
Kill 1000 Enemies