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