Once you place all the Chozo Artifacts on the Cipher, Meta Ridley appears. The first part of the battle is not too difficult. Meta Ridley flies around the arena, trying to attack you with his missiles and Pulse Beam laser he shoots from his mouth. Most of these attacks are predictable, so you should be able to avoid them. When he lands, aim straight for his chest and shoot charged Plasma Beam shots. Keep your distance from him and save your Missiles for round 2.
Round 2 takes place after you destroy Meta Ridley's wings. He is forced to stay on land, but that doesn't affect his agility. Meta Ridley will charge at you and then spin around, hitting you with his tail. Dodge this maneuver by side dashing twice, then turn around, lock on, and jump over his tail swipe. With practice, you will be able to avoid this attack completely. It is important to avoid since this attack can hit you up to three times.
Attack his mouth when it's open - use the Wavebuster if you acquired it. This will push Meta Ridley backward, causing the plate on his chest to open up. This is when you should break out a Super Missile (or stick with the Wavebuster). If you run out of Missiles, use charged Plasma or Wave Beam shots.
If this is the first time you fight Meta Ridley, there's a very good chance you will die. Make sure you go in with 100% Energy and Missiles - use your Gunship to get all this back quickly.
Like all bosses, Meta Ridley is a rare scan.