After some trials, I have determined that stage 4-4 (Keesi III boss stage with purely air enemies) is the least stressful and highest-yielding stage for stars.
I can usually get 50k+ stars each round, though I quit until I get 60k+. Clearing gives you only 2k stars but the stage itself makes up for it. In contrast, 5-4 usually gives 30k+ points (and 5k for clearing). I have not experimented with 5-1 (which is farmable as I did get high stars when I tried it) but that stage can be incredibly stressful, and UFO Invader is my key unit on that stage (very few people would have bought that)
Units[]
The key to this stage is to kill off as many helicopters as you can before they fly off (Future Shobu doesn't fly off). SNK seems to have given them high star yields to compensate for them flying off against a suboptimal deck. Keesi III dies quite easily and isn't that big of a threat, just keep walls around to protect your base in case its hp gets low.
Key Units/Helicopter Slayers
These units will kill all flying units (except Keesi III) in one hit.
Christmas Fio (300 medals, ugh, but she's very useful both online and offline)
Wrath Allen
Secondary helicopter Slayers
These units need two hits to kill flying units but still contribute significantly.
Zombie Fio (fastest zombie, higher chance of avoiding bombs)
Elephant Slug
Samurai Infantry(Red) (more for stalling but the fact that he attacks after dying is great)
Walls
Mars Mecha (cheap and more spammable)
Augensterm ver. P.M. (can also kill helicopters with the special, but it dies fast while being bombed, so it's more of a wall here)
Misc
Keesi II (shields your base from Keesi III, special can clean out helicopters if your ground units keep getting bombed, and also does crazy damage to Keesi III)
Ring Laser Mecha(Red) (special is anti air, but somewhat slow and needs to hit a few times, so it's mostly for backup)
Filler
Choose any anti air unit here, except Bradley PM (since it targets the invincible Hi-Dos). Examples include Fat Fio, Winged Invader and Zombie Tarma. If you use Zombie Tarma, don't over-rely on him as his slow walk speed makes him vulnerable to dying from bombers.
== Procedure ==
The idea is to rack up AP for Wrath Allen as soon as possible.
Start with 2 AP upgrades and send out Christmas Fio. Upgrade AP once more after she is sent out. Time her special such that she hits as many helicopters as possible. There is low chance you will immediately get 900 AP and can get Wrath Allen out, but it's more common that you need to wait a bit. Sometimes you will end up very little AP (if the AI sends out Samurai Planes and Huge Locust to open) so either restart or use Red Samurai to stall for a bit. If Keesi III uses its special, you can send out Mars Mecha to protect the base.
Once Wrath Allen is out, you're mostly set. Your next goal is to get Christmas Fio out again, but this time you can protect her with a wall. Another special and you'll get tons of AP. The rest is spamming units and timing their specials while half your units get bombed off. Try to send Keesi II out when you can: it shouldn't be too difficult as Wrath Allen and Christmas Fio's specials rack up tons of AP when they hit multiple helicopters. Christmas Fio is your most important unit after Wrath Allen, so try to send her out with walls. Use Zombie Fio and Elephant Slug's specials whenever they can hit helicopters.
MSAs can be used to eat helicopter rocketss and protect Christmas Fio for a short while.
WATCH OUT for the evil slope in the middle of the map that eats Christmas Fio's special! It's where the terrain changes.