Nope there's no secret trophy for beating gná without damage but you'll get the true queen just for defeating her, damage or not. Worth noting that a lot of players try no-damage runs as personal challenges, and you'll find some pretty impressive videos of that online if you're interested in seeing how it's done

Going for a no-hit run is definitely doable with enough practice, and you'll need to master dodging her attacks, timing your spartan rage carefully, and knowing when to use the leviathan axe. While it's not something the game tracks officially, it's a great way to prove your combat skills if you're up for the challenge. The main thing is just getting that the true queen trophy which only needs you to win the fight, no special conditions needed