Here is the full list of all 14 King of the Couch: Zoovival achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Win with every class.
Play a game with only gunslingers.
Equip every weapon.
Play a game with only santas.
Play a game with only ninjas.
Play a game with only cooks.
Play a game on every map.
Play a game with only mad scientists.
Play a game with only construction workers.
Win a Go nuts game with only Stealth.
Win a Go nuts game with only Swapgun.
Win a Go nuts game with only Mexican Standoff.
Win a Go nuts game with only Bats.
Win a Go nuts game with only Katanas.