Was TAARNA the first?

Nope. Taarna was from Heavy Metal the movie, but the story arch she takes up was based on a comic from the magazine called Arzach, and the hero in that comic was a bundled-up man. The only thing that stayed more or less true in the movie was Den of Neverwhere, and it only differed cuz the Loc-Nar become the primary antagonist that binds the film together, and you see a lot less of Den's dick in the movie!

When Marvel comics first introduced Red Sonja in the Conan comics, she sported red silk shorts with belt, short-cuffed boots, coins-on-string (the Hyborian equivalent of a coin purse) and a simple mail shirt (this). It was only when the artist showcased the sexy pin-up he made during a comic convention did the design become such a hit, they put her into the outfit in the comics.  But that was in the mid-'70s, and this character did not come form Robert E. Howard's yarns -- his action chicks were Valeria of the Red Brotherhood and Red Sonya of Rogatino (not the same as Red Sonja in any way), and they were both dress as pirates. Although most people reject Red Sonja's "chainmail bikini" as in inappropriate for battle, but if one looks at like as a suit made of coins (the whole outfit is made of metal disks connected by wire), than one could see it as the wallet of a nudist warrior. Speaking of which...

One of oldest she-fighters in fiction to fight in "negligible covering" is Dejah Thoris from A Princess of Mars. Although a total nudist in the books, later artists like Frank Frazetta, with the need to keep the covers modest, would exaggerate the jewelry Dejeh carries to create an outfit that would latter inspire Princess Leia's slave outfit, and lots and lots of other cheesecake outfits like it. So as far as modern, western fantasies goes, she could be the first... and most influential! A Princess of Mars inspired so may sci-fi writers, which spread into countless comic books and movies!
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P.S.

As for "chainmail bikinis", that is one of those things that are completely impractical in combat, but fantasy always take great liberties with how characters conduct combat, that it can easily be passed off as a "genre effect", much like how Stormtroopers can hit Rebel Troopers and Jawas with great accuracy, but turn walled-eyed when they see the heroes. I once did a tongue-in-cheek blog post that stated that a character could get full armor protection form armor that was reduced to a two-piece bikini for women, or a cod-piece for men if the characters are sexy enough, and noted some (make and female) visual examples. But like I said, it was for shits & giggles.