Here is the full list of all 40 Monster Outbreak achievements.
Collect a fire stone
Kill 100 monsters
Kill 1,000 monsters
Kill 100,000 monsters
Kill 100 monsters with structures
Kill 1,000 monsters with structures
Kill 100,000 monsters with structures
Kill 500 monsters with your sword
Kill 200 monsters with an axe
Kill 500 monsters with a bow
Kill 200 monsters with a hammer
Kill 1,000 monsters using fire towers
Kill 1,000 monsters using wooden spinners
Kill 1,000 monsters using crossbows
Kill 1,000 monsters using cannons
Kill the Slime King
Kill the Golem
Kill the Undead King
Kill the Trickster
Kill 1,000 invaders
Kill 500 dimensional harpies
Kill 500 devourer giants
Kill 500 beholders
Kill 500 scorpions
Unlock every structure
Unlock every character skin
Unlock every pet skin
Unlock all the maps
Unlock all undead maps
Unlock all lava maps
Collect 10 ghost flowers
Collect 2,000 logs
Collect 10 magic rocks
Collect 2,000 rocks
Collect a beholder eye
Collect an ice stone
Collect an electric stone
Reach wave 20 on any map
Reach wave 50 on any map
Reach wave 100 on any map