Here is the full list of all 12 Breach achievements.
Accumulate 500 XP through combat missions
Accumulate 2500 XP through combat missions
Accumulate 7000 XP through combat missions
Accumulate 16000 XP through combat missions
Accumulate 32000 XP through combat missions
Accumulate 48000 XP through combat missions
Get 100 kills playing the Rifleman class
Get 100 kills playing the Gunner class
Get 100 kills playing the Sniper class
Get 100 kills playing the Support class
Get 100 kills playing the Recon class
Crush 30 enemies with structural collapses