This sidequest in Chapter 3 of Final Fantasy VII Remake can only be unlocked after completing the Nuisance in the Factory quest.
When talking to Gwen, you will learn that a Cerulean Drake has made its home in the abandoned factory. However, you'll need a Watch Security Key to gain access first.
Finding the Watch Security Key
Head back to the factory, in particular the section containing the bench and vending machine. You'll find the key in a crate there, so break them and pick it up.
Now, head back to the room in which you fought the Lesser Drakes. You can now open the locked gate with the key by approaching the green panel to the side.
You'll enter an arena of sorts containing the Cerulean Drake. For this fight it's highly recommended you have the Aero spell, so if you haven't already, make sure to complete Battle Intel Report #2 first and obtain the Wind Materia.
Aero will do a lot of damage here, and build the stagger gauge quickly. Make sure to keep your health topped up, and switch characters often so you can cast more magic. When it's at ground level. hit it with all the physical abilities you have.
This can be a tough fight, but as long as you're mindful of when to guard and heal, you should be okay.
Once the Cerulean Drake is defeated, return to Gwen and complete the quest. You'll receive a Star Bangle accessory and have your HP and MP restored.
Now you can continue with the main Chapter 3 story.
