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