Patient Gamers

Napple Tale: Arisa in Daydream
A game for the Dreamcast that had a primarily female dev team. It was exclusive to Japan, but a translation patch was released a couple years ago.

Atelier series
There are a bunch of these. They’re RPGs based heavily around crafting. Actually, they basically pioneered crafting in RPGs.

Um Jammer Lammy
A spin-off of Parappa the Rapper. Lammy has only 15 minutes to make it to her band’s performance, but getting there won’t be easy.
Note that Stage 6 is censored in the North American release. Also as a bonus, completing the game unlocks Parappa mode, with new versions of every song after Stage 1.

Athena
Stick with the original arcade version. The NES port is infamously bad.

Psycho Soldier
A spin-off of Athena (sort of) starring Athena’s descendant/reincarnation (it depends on the writer), Athena Asamiya (and Sie Kensou as player 2’s character). Athena (and Kensou) would later become staples of the King of Fighters series. The game is notable for being the first game with a vocal soundtrack.

Baraduke
An arcade title from Namco. Being on this list is actually a pretty big spoiler because the fact that the protagonist is a woman isn’t revealed until the end of the game. Now that probably sounds like a ripoff of Metroid, but here’s the thing: Baraduke did it first.

Koudelka
An obscure horror RPG for the PlayStation.
The game is an unhappy compromise between the creator and the dev team. One side wanting to make a survival horror game and the other going for something like Final Fantasy VII. I’ve never actually gotten very far in this one because I hate the battle system. Also, this game has connections to the later Shadow Hearts series.

Literally every game in the Otome genre
Probably not what you’re looking for, but technically fits your criteria of having a female protagonist.

I might add more to this post if I can think of something else.