Here is the full list of all 15 Swarm Arena achievements.
Score 100.000 points without getting hit
Beat Pandora with Learning set to "Normal" by "Title Rules, 10 Wins"
Beat Pioneer by "Title Rules, 3 Wins"
Beat Jester by "Title Rules, 3 Wins"
Score 100.000 points
Play 20 rounds against another human
Have 3 or more Steam Friends with a highscore in Swarm Arena
Beat the Teacher by "Title Rules, 3 Wins"
Play the Tutorial
Score a total of 1.000.000 points in 3 games or less
Score 1.000.000 points
Train Pandora to beat Genesis by "Title Rules, 3 Wins"
Beat Genesis by "Title Rules, 3 Wins"
Get to the top of your Friends Leaderboard while having at least 3 Steam Friends with a highscore in Swarm Arena
Get a Score Multiplier of 250 or more