master ball, paralyze and block, false swipe and random balls
You randomly find Latias in Sapphire version. If you don't catch it the first time you see it, you can go to your poke'dex, select Latias, then chose area and it will show you where Latias is. But, you must get there quick because it could go somewhere else if you are too slow. It gets annoying after a while so be sure to g fast. Also, say the first time you find Latias you burn it, then it flees, the second time you find it, Latias will still be burned. So just keep hurting and chasing Latias until you can catch it. However, you can't find Latios in Sapphire version.
Use the EXP Share and keep on doing the elite four. Also, try getting rare candies! Latias should be at a high lvl soon.
Leprechauns are pretty fast, but you should be able to catch them if you have a complex trap.
It's not A Raikou, its Raikou, as you only get one/two chances of battling him/her and it's legendary I would recomend getting it down to barley any life left and asleep. Catch with a fast ball
Latios AND Latias variate routes, if you go to the weather tower you can see which route Latios is on by talking to somebody, 'I'm not sure who but if you don't get to that route fast enough Latios will have gone, if you don't catch him and he escapes (as long as you don't kill him) you will have another chance to catch him
The easiest way to catch all the Pokemon is to start with the Pokemon with the lower levels and continue until you reach the highest leveled ones(which is rayquaza, kyogre, groudon and maybe latios OR latias
usually on thursdays from tilt village call supercharged latias/latios.honchkrow will appear in front of you he is quite fast so you will need to boost latios/latias (touch latios/latias while flying to boost).
U need the event dogs but u only need one if u are fast today entei is available on heartgold and silver and tomorrow another dog is available
Have a Fast Ball with you. This ball should catch at first time. If not, stack up on Ultras.
Try teaching a fast Pokemon Mean Look.
you give Kurt the apricorn dude apricorns and if you are lucky they will turn out to be fast balls
To get them I suggest you get a Pokemon that knows mean look.Then get lots of fast balls.Hope this helped :)