Upon entering the Hanging Gardens, you'll immediately notice the vibrant flora and the presence of new enemies: Peckers. Peckers are flying creatures that swoop down to attack. Use your Breaker's Bow to shoot them out of the sky before they get too close. They can be annoying in groups, so prioritize them.
You'll also encounter Windbags, stationary enemies that inflate and explode, dealing area-of-effect damage. Keep your distance and use ranged attacks, or hit them quickly with a melee weapon and dodge away before they detonate. The path will involve some platforming over gaps; remember your dodge roll is key for these sections. Look out for hidden paths that might lead to extra Fragments or crafting materials.