You can see your milestones in the "Key Performance Indicator Terminal" (KPIT) in your room (aka the place you initially load into). Its the computer monitor to your front-left before exiting your room into the main hub.
Milestones are basically extra goals and activities to do during missions, like completing missions in certain biomes, completing missions with certain mutators, gaining levels with a class, or unlocking a certain number of accessories. The KPIT will show progress for each milestone, and will say "Completed" when ready to turn in. Simply click on the completed milestone to get the perk star reward (used to unlock perks). Do this 10 times to unlock the achievement.
The good news is that you'll unlock Milestones pretty quickly without really trying, and will easily get to 10 by about Player Level 5 or 6.