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