Oh wow, this is a pairing you don't stumble on every day. Honestly, I've always thought the concept sounds like a recipe for disaster—I mean, we're talking about Percy Jackson, the guy whose main trait is hating the gods, and Hera, literally the goddess of marriage who actively dislikes heroes. The few fics I've seen that make it work tend to lean heavily into the enemies-to-lovers trope but with a cosmic, mythological scale. There's one called 'Queen's Gambit' I vaguely remember that sets up a scenario where Percy is forced into some kind of political alliance with Olympus, and Hera is his designated handler. It played with the tension between duty and genuine, grudging respect pretty well. The writing was a bit uneven in places, but the author nailed Hera's regal, icy demeanor slowly thawing.
What's tricky is avoiding making Hera seem wildly out of character just to force romance. The best ones keep her formidable and proud, and Percy stays stubborn and irreverent. It's less about sweetness and more about two immensely powerful wills clashing and eventually finding a strange, uneasy alignment. I'd check tags for 'arranged marriage', 'political marriage', or 'forced proximity' on AO3—that's where most of the decent attempts are hiding. You'll have to sift through a lot of... less successful takes, though.