Here is the full list of all 24 Laser League achievements.
Unlock all other Achievements
Reach Prestige rank 01
Reach level 20
Reach level 10
Level up for the first time
Reach Mastery rank 5 as any Class
Reach Mastery rank 2 with all base game Classes
Finish a match as MVP 10 times (Online Play)
Finish a match with the highest revive streak 5 times (Online Play)
Finish a match with the highest elimination streak 5 times (Online Play)
Win 50 matches (Online Play)
Win a match without the opposing team scoring a point (Online Play)
Activate 5000 Laser Nodes (Online Play)
Eliminate 1000 opponents (Online Play)
Revive 500 teammates (Online Play)
Eliminate 2 opponents with a single expanding Laser (Online Play)
Hit 3 or more opponents in a single Smash ability use (Online Play)
Traverse 4 or more opposing Lasers in a single Ghost ability use (Online Play)
Steal 4 or more Laser Lodes in a single Thief ability use (Online Play)
Teleslice 2 or more opponents in a single Snipe ability use (Online Play)
Shock 3 or more opponents in a single Shock ability use (Online Play)
Slice 2 or more opponents in a single Blade ability use (Online Play)
Win a match (Online Play)
Complete the Tutorial