Here is the full list of all 45 Super Kaiju achievements.
This is a test achievement
Unlock all cards
Gather 150 stars in a single battle
Hit your opponent with 10 non-homing bombs in a match
Use one of each turret in a match, and win
Take out the opponents shield with an EMP and then launch a missile barrage
Fill your pool of stars to the limit
Disable opponent weapons and attack with mortar and drone
Destroy the opponent’s turret
Gather 50 stars using secondary weapon in a match
Win your first multiplayer game
Challenge a friend and beat him
Win a round by taking their health to 0 as opposed to time out
Win a round in less than 90 seconds
Tier up at least once
Reach gold tier in a season
Use every single card at least once
Beat the AI on highest level
Kill 15 chair monsters in a battle
Win a round with no more than 10% health left
Win a round with 100% health left
Kill 10 monsters where your opponent caused more than 50% of the damage
Take out 100 incoming bombs in a match
Reach diamond tier in a season
Kill a total of 5000 monsters
Gather 5000 stars
Take out 4 monsters with a single bow shot
Win 20 multiplayer matches
Win 10 matches using each Kaiju
Block all missiles of 10 missile attacks using the shield
Take out all missiles in an incoming barrage
Finish at top rank in any season
Finish at top rank in 3 seasons
Win 50 multiplayer matches