So you want to find quiet?
*** Spoiler - click to reveal ***
Start the Spec Ops level 6 that has you searching for a Stun Arm blueprint. Pick the Helicopter drop that is west of the mission point (The drop that looks like it is closest doesn't work no matter what because you can't get over the mountain). If you follow the road out of the mission area, the first area you can drop on that road is the one you want.
Now jump on D-Horse and follow the road toward the mission point. About a 1/3 of way there you will come across some ruins. Someone will try to snipe you and the game will let you know you're starting episode/mission 11 (does this on its own). You will now get into a sniper dual with Quiet (which is amazing).
Once you win the battle, run to her location and you will have a choice whether to kill her or bring her to Mother Base. DO NOT SHOOT HER! Which will then automatically start the cut scene where you are lifting her into the chopper.
- If she is not at the location where you dropped her, then run back to the middle of the area/ruins and she will be lying there.
After dropping her off at Mother Base, Do a mission or two then go back. There will be a cut scene. Go do another mission or two and when Ocelot calls yous and tell you to come back to the base (the spec ops mission 111 - "Visit Quiet" becomes available), accept and go back to Mother Base again and she should be ready to deploy and be your best buddy.
Tips for battle -
1) Mark her with the binoculars. Use your weapon to find her then use the binobulars. You will see a little shimmer of light (like a mirror reflecting), that is her. Also if you see a rainbow and some sprinkle like stuff, that is also her.
2) If you just can't seem to beat her, you can use a supply drop and drop it over her head. Doing this 2 or 3 times will win the battle for you. I DO NOT RECOMMEND this method unless you are truly having issues because this battle is so much fun!
(Copied A Xbox One guide)