Flashgal's opening level makes it look like it's going to be a Kung-Fu Master
clone, but it actually expands into a variety of level types as you get into it. Our rather suspiciously Elektra-esque heroine will fly in a helicopter, ride a motorcycle, ride a jet-ski and apparently even travel back in time to feudal Japan to wield a katana before all is said and done.
The game doesn't really give you much of an in-game story, but from context apparently Elektra/Wonder Woman has had it with Chibi Kingpin's criminal exploits and is hunting his ass down. He shows up as the boss of every level starting with the third one, usually appearing to fire a powerful gun repeatedly while surrounded by infinitely respawning mooks that keep rushing you.
The gameplay is decent for 1985 standards, a bit on the jank side sometimes but you can find much worse in the arcade roster of this period. The main compelling quality of Flashgal is simply its quirky weirdness. It was clearly inspired by popular comics of the time, particularly Daredevil given the mini-Kingpin villain and the main character's visual design. But there's all sorts of random stuff tossed into the soup too in the fine Sega arcade tradition of the '80s, like the wild ostrich enemies that turn into a rump roast when defeated. Said ostriches also sometimes randomly drop a gun, and one of the best little meta touches in the game is that there's a huge Trojan warrior sub-boss who appears in some levels, but he'll immediately turn tail and run his ass away if you've got the gun when you reach him!
The fighting / sword-wielding levels work a lot better than the vehicle levels, since there's a margin for error as you have a health bar (which seems to replenish as you beat up certain enemies), whereas collision with anything in the vehicle levels burns a life. Nothing about the game is all that difficult until near the end, as you can brute-force your way through with the Power of Quarters thanks to a generous checkpoint system. The eighth level, which puts you on a jet-ski, has checkpoints that are spaced out further and is just absolutely brutal. Though the game isn't fantastic, it was solid enough that I was interested in continuing to play up to that point just to see what weirdness would come next, but the jet-ski level is just far too nasty to keep throwing yourself at.
Pretty sure some of this team later went on to do the Streets of Rage games, as Flashgal bears more than a passing resemblance to Blaze, and a number of enemy concepts appear to have been recycled as well. Sword-wielding Flashgal may have also lent some inspiration to the design of Tyris Flare from Golden Axe.