This requires Human Link and the Stone Mask.

If you do not have the Stone Mask, the whole process of getting past through the pirates will be hard and you might have to start all over to get back on your task. Don't give up just yet. To obtain the Stone Mask, there's a unseen Soldier in the Canyon surrounded by rocks. You will need to use the Eye of Truth. Give him a Red Potion or Blue Potion to restore his strength. Milk does not count for whatever reason. After he thanks you, he will give you the Stone Mask. Wearing this mask will make you invisible to most enemies. Certain enemies can detect you and hurt you (ie. Minibosses and Bosses). However... the Gerudo Leader will also detect you (while attempting to get the Hook Shot in that room but you will get thrown out instead).

The Stone Mask will help a lot if you don't wish to be caught so easily. For one, the Gerudo Pirates will be walking around with their halberds, and even when you get close to them with the Stone Mask on, you can slash them with your sword. They will see you but will not throw you out. However, the Gerudo Elites are not fooled by the mask you are wearing. You will be fighting against them. Beat them and get the Zora Eggs in the next room.

The rest of the Zora Eggs are hiding someplace else in the ocean if you're wondering.

Good luck on your adventure.