There are four Zeta Metroids in the game, and while they are less powerful than Omega Metroids, they can be quite formidable in narrow confines, making them in some ways more deadly. Zeta Metroids will charge at Samus relentlessly, rushing through the air at very high speeds. For this reason, they are much easier to defeat with the Screw Attack - in fact, this item is almost essential to the task.
The brute force method is to use the Screw Attack to fly circles around the Zeta Metroids, pummeling them with Missiles when you see an opening. Of course, this is easier said than done, particularly in rooms with tight spacing or that are covered in spikes. Zeta Metroids can be defeated with 20 Missiles.
You can also take advantage of the Zeta's algorithm for flying directly at Samus. One good technique is to jump and fire one or two Missiles while standing right next to the Zeta, then crouch to avoid its fireballs and swooping attack. The Zeta will fly over you, letting you turn around and repeat the process.
The first Zeta Metroid you should encounter is in the front entrance of the large tower in Ruins Area 4, right before collecting the Screw Attack. When you encounter the Zeta Metroid, it is highly recommended to quickly Space Jump up through the ceiling; here, you'll come to an item room containing the Screw Attack. If you don't collect it, be prepared to lose a bare minimum of 150 energy.
The most troublesome Zeta Metroid is in the sand pit in the caves outside Ruins Area 4. When you enter a room full of sand, more forward cautiously, clearing out the sand above and in front of you to give you some maneuvering room. You will eventually encounter a Gamma Metroid in the process of molting. Once you are prepared, approach it to begin the fight. One good trick is to lead the Zeta Metroid to the entrance where you can pump it full of missiles rapidly.
