Here is the full list of all 25 Let Them Come achievements.
Moving on
2 active bonuses at the same time
You killed 10 enemies at once!
1000 Enemies Killed!
100 Enemies Killed!
You completed the game tutorial
Thank you for your support!
You have come to the end but new challenges await!
5000 Enemies Killed!
10 000 Enemies Killed!
5 Challenges Completed
20 Challenges Completed
50 Challenges Completed
100 Challenges Completed
You completed a wave using only secondary items
You completed a wave using only genades
You killed 100 enemies in a frenzy!
You discovered all the alien species
You finished campaign on highest difficulty
4 active bonuses at the same time
Perfect combo bonus!
Game plus mode completed