So you know how to beat Quiet for her recruitment mission the honorable way, but have you ever considered that you don’t have to deal with her for however long of a battle just to make sure she doesn’t die? That’s right, put that awful tranquilizer gun away (because you definitely don’t have a tranq sniper this early on), you can end her with supply drops.
At the start of the battle, when you’re behind the fallen wall, mark her with your binoculars so you see clearly on your map where she is. Then, go to the Supply Drop menu and choose the cheapest thing to drop right where she’s located. I went with the cheapest handgun, but really, any bonk will do. Go nuts, it’s hilarious any which way you do it.
It only takes two hits with this method to down her as though you had filled her with tranquilizer darts. After that, she’s recruitable or killable, the choice is yours. Congratulations on playing dirty.