FYI: the achievement description is misleading. What it should say, is, "Complete 20 Veteran MAIN Missions". Before you can take on a veteran main mission, you have to complete 3 veteran side missions. So doing the math, you can tell this is going to take a while to complete. On the bright side, you need 10,000 kills and you need to finish 100 missions without anyone going down anyway, so there's that.
EDIT: Great tip from ailurophile in the comments, makes this go by extra quick:
Worth noting that the progress counter goes up as soon as the mission ends, you can therefore hit restart mission at the screen before returning to the convoy and effectively skip doing all the side missions.