Here is the full list of all 42 Combat Monsters achievements.
Finish the easy quest
Realtime or Async
Do your first rank up
Finish the introductory quest
Collect every Human
Collect every Elf
Collect every Orc
Collect every Dwarf
Collect every Golem
Collect every Zombie
Collect every Lizard
Collect every Minotaur
Collect every Werewolf
Collect every Elemental
Collect every Cyclops
Collect every Monster
Collect every Hero
Finish the medium quest
Finish the hard quest
Have three people use your code
Have five people use your code
Have 10 people use your code
Collect every Skeleton
Finish the even harder quest
Finish the insane quest
Collect every Robot
Collect every Imp
Collect every Spectre
Collect every piece of Armor
Collect every Weapon
Collect every Shield
Collect every Spell
Collect every Rune
Collect every card (plain or foil)
Collect every foiled card
Collect every Vampire
Finish the 1v2 quest
Collect every Goblin
Finishe the 2v4 quest