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