Here is the full list of all 25 Smash Up achievements.
Have a minion on every base
Score two bases at the same time
Play King Rex twice two times in one game
Be the only player with cards on a base when it scores
Complete the tutorial
Score your first base
Win a game playing with the Zombies faction
Win a game playing with the Dinos faction
Win a game playing with the Aliens faction
Win a game playing with the Ninjas faction
Win a game playing with the Geeks faction
Win 10 games either offline or Online
Win a game playing with the Aliens and Geeks factions
With the game with a 10 or more point difference
Get 10 or more points from a single base
Win a game playing with five different factions
Play the boss minion from each of your factions in the same turn
Come first on every base for the whole game
Win the game without being first on any base
Win a game playing with the Pirates faction
Win a game playing with the Robots faction
Win a game playing with the Pirates and Robots factions
Win a game playing with the Tricksters faction
Win a game playing with the Wizards faction
Win a game playing with the Wizards and Zombies factions