After you grab your gear there is only one main objective:
Get to the extraction.
Other objectives are side objectives and can be skipped.
About 60-70% of the way through the map you'll start seeing vehicles you can use. I recommend you use one to get to the end.
Once there you will have to clear out two Anti-Air guns and pick up some documents. I recommend staying in the building of the documents and just using your automatically recharging Airstrikes. Not only for the achievement but also for convenience. At one point a helicopter will spawn and after that 3 others will soon join. Once you take them out and clear any remaining enemies you will do an autoscroller helicopter ride. Shooting here is optional. Once you see the stats menu and the credits start to roll your achievement will pop and you will only have 2 more playthroughs to go