Story Achievements
You'll unlock Surgical Strikes and The Greater Good just by completing the main storyline.
You'll Unlock New Recruits by completing the side quests Rise of Shaqilat and Shadows of the Scarab.
Feat Achievements
Walls of the Ruler– Complete all location objectives for the fortress of the same name, which you might as well do during the story quest of the same name
What Time is It? – Leap of Faith off the Arsinoe sun dial between 10am and noon. Noon is the open doorway, and 10am is two ticks before that.
Zip It Off– Perform three assassinations off a zip line. The east end of the Operum Tuorum Gemmam Castra camp (where you kill Tacito) is ideal for getting this achievement- there are several ziplines, and you'll usually pass over several candidates on the way down.
Prison Break – Free 20 rebels. The Sinai is lousy with caged freedom fighters, but if you find yourself short, try revisting Operum Tuorum Gemmam Castra, which has several rebel cages. Also, in the Sinai, caged rebels will generate 'Assist the Rebels' exclamation points, just like rogue animal attacks, et al.
Team Play – Headshot an enemy while Senu is harassing them. If you headshot a lot of people, you may get this one without even trying. Otherwise, just designate someone for Senu to hassle, then shoot them in the head.