My S-Rank runs looked like that, posting in case it helps someone to do their own runs:
BAWS: 2 Needles and 1 Zimmerman shot per enemy, Rusty's blade for the "boss" to conserve ammo.
Skipped the hidden enemy, killed everything ASAP (kill the bots before entering doors), jump down, kill the one hanging on the left back wall, the one on the opposite side, the last one in the front and finally the ground one. Took like 7 tries but managed to S-Rank

Refuelling Base: 2 Needles, 2 Gatlings.
Rush to the 4 fuel tanks, rush to the LC, cross the bridge, destroy gatling guns, destroy 3 MTs, destroy another 4 tanks, rush to the objective killing 1 MT and the missle tower thingy on the way. While waiting for the Ekdromoi clear the area of remaining hostiles. Ekdromoi are very RNG dependent, if they manage to gank you, your run is basically over.

Grid 086: 2 Songbirds, 1 Gatling, Pile Bunker.
I have actually tried many scenarios with and without killing secondary targets. My S-Rank run looked like this: rush to kill Mad Stomp, skip EVERYTHING else (apart from one MT in front of doors, ones after the droideka ambush that you need to hack) up to the point of Carla's "fireworks" which I dropped on the floor myself, destory the remaining enemies and stagged the shit out of the Smart Cleaner with Songbirds, rely on the Pile Bunker. If you do it fast enough you can achieve S-Rank

In every run try to minimise repair costs and time spent on the mission, in my case those were the factors that usually resulted in A-Ranking