Man, the struggle is real. I spent ages looking for good 'Big O' fic that wasn't just rehashing the amnesia plot or Roger and Dorothy's weird tension. I wanted the giant robots, you know? The actual Paradigm battles. AO3's tag system saved me—you gotta search for 'Paradigm fights' or 'mecha action' in the fandom tag and then filter. Found this one author who writes these incredible technical breakdowns of each fight, like they're a sportscaster for giant robot wrestling. It's not a huge fandom, so you have to dig, but the gems are there. I'd also check older archives like fanfiction.net, but be prepared to sift through a lot of 2003-era angst.
Honestly, the best battle expansion I found was a crossover with 'Getter Robo' that had Big fighting off an invasion of Dinosaur Empire troops in Paradigm City. It was gloriously dumb and exactly the over-the-top spectacle the show sometimes hinted at but never fully delivered. Sometimes you have to look outside the pure canon to get the good robot-on-robot action.