Things You'll Need
Instructions
The First Hunt
Before anything else, you will need to defeat "Pokemon Ruby's" end-bosses, the Elite Four. Latios and Latias cannot be encountered until you have done this. This is a test of endurance, so bring a large inventory of healing potions, revives and condition-curing items, such as Dethaw or Flute. Once the last of the Elite Four has fallen, May will appear and give you some tips to defeat them, only to realize that you already have. Save your game now.
The game will teleport you back to your hometown, where Professor Birch will give you a National Pokedex and a news report for you to check will appear on the television. Go ahead and do so. On the television will be a news report detailing a new monster that has been spotted flying over Kanto. You can leave your hometown now and head toward the Safari Zone. On the way there, stock up on Repels and Ultra Balls.
You will need to acquire a Level 39 Wobbuffett and set it as the leader of your party. The level is very important, because Latias appears at Level 40 and the Repels you will use drive off monsters that are a lower level than your party leader. With Repel activated, wander around in Safari Zone brush. There is no pattern or skill to causing Latias to appear, so keep at it until you get lucky enough to encounter him.
Capturing Latias
If you have not already used your Master Ball, use it now. This will instantly capture Latias, in which case you can skip to Section 4. If you do not have a Master Ball, you will need to use Wobbuffett's Shadow Tag or a Golbat's Mean Look to prevent Latias from running from the battle, which it will otherwise attempt to do on the first turn.
Once Latias has been trapped into fighting, prepare to carefully whittle down his HP. Using Grass-type Pokemon against him is recommended, as their moves are not very effective against him and so prevent you from accidentally doing too much damage and killing him. Status-inflicting attacks, such as Deep Freeze or Fairy Dust, can prevent Latias from attacking you and make him easier to capture, so use them as often as you can.
Once Latias is around 20 percent HP and preferably has had Frozen or Sleep status inflicted on him, you will begin to try to capture him. He is very good at escaping from your capture balls, so you will need to keep at it. On occasion, it can take as many as 40 Ultra Balls before you finally trap him. Should you get unlucky and run out of Ultra Balls, you will need to run away from the battle. Defeating Latias will prevent you from ever encountering him again.
The Second Hunt
If you were unable to encounter Latias the first time, don't give up. Now that you have encountered him, your National Pokedox will be able to tell you where he is, making it a lot easier to track him. Restock on Repels and Ultra Balls, check your Pokedex for his current location and walk to the city nearest him. It is important to walk, as flying will cause him to teleport to a different, random location.
Stop for a moment and consider your method of approach. Latias moves in a logical pattern, which is to say he can only move through adjacent routes. Every time you change zones, he changes zones, as well. For example, if you move onto Route 23 and he is on Route 24, he will either move to Route 23 or Route 25. Use this logic to try and trap him onto the same route as you.
Now that you have encountered Latias again, use the same method for fighting him as outlined above. If he escapes again, repeat this entire process. If you manage to capture him, his brother will be the next target. Using the Eos ticket you should have already acquired, set sail on the S.S. Anne toward the Southern Islands. Latios waits for you there.
Capturing Latios should be undertaken using the same exact methods you used to capture Latias, except that it is unnecessary to use Mean Look or Shadow Tag to trap him. He will not try to run away. Unlike Latias, Latios will never occur anywhere else in the game should you be forced to run away or are defeated by him, so save the game beforehand. Eventually, you will capture him and can move on to finishing up the rest of your Pokedex.