Here is the full list of all 15 Swarm Arena achievements.
Beat Jester by "Title Rules, 3 Wins"
Score 100.000 points without getting hit
Score 100.000 points
Beat the Teacher by "Title Rules, 3 Wins"
Play the Tutorial
Beat Pandora with Learning set to "Normal" by "Title Rules, 10 Wins"
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"
Have 3 or more Steam Friends with a highscore in Swarm Arena
Play 20 rounds against another human
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
Beat Pioneer by "Title Rules, 3 Wins"
Get a Score Multiplier of 250 or more