Lugia its easier.
you can catch lugia in whil islands in heartgold
Ho-Oh Lugia Suicune Articuno Zapdos Moltres Mewtwo Kyogre Raikou Entei Latias
catch him at lvl 70
you can catch buizel by going to the safari zone but before you need the national dex before that and must have caught ho-oh,lugia and mewtwo.
You can't catch Mewtwo in Pokemon Diamond and pearl and also platinum. But you can catch Mewtwo in heartgold and soul silver
if you dont wanna waste your master ball, then the strongest ball will be the Ultra Ball...
You can only catch lugia if you migrated it from firered or leafgreen. If you want lugia get one from heartgold or soulsilver version.
Cerulean cave
Typically speaking, you want to save your Master Ball for either Lugia (HeartGold), Ho-oh (SoulSilver) or Mewtwo. This is because in HG, Lugia is Level 70, in SS, Ho-oh is Level 70, and in both, Mewtwo is Level 70. Granted, you will be tempted to use it on Raikou, Entei, or Suicune, it's best not to. They are Level 40 and much easier to catch with Ultra Balls than either Ho-oh, Lugia, or Mewtwo. However, if you manage to catch Lugia, Ho-oh, or Mewtwo with an Ultra Ball, and still have your Master Ball, you're certainly encouraged to use it as you see fit. Again, this is merely a suggestion, your decision is still up to you.
You can't catch Mewtwo in Gold, Silver, or Crystal. But you can catch it in HeartGold and SoulSilver in the Cerulean Cave at Lv70.
In Pokémon HeartGold, the Legendary Pokémon that you can catch in it are Articuno, Zapdos, Moltres, Mewtwo, Raikou, Entei, Suicune, Lugia, Ho-Oh, Latias and Kyogre. You can also catch Latios if you have the Enigma Stone which is only available via a Nintendo Mystery Gift event and you can also catch Rayquaza if you have the Kyogre from "HeartGold" and the Groudon from "SoulSilver."
You can catch Lugia in the gameboy games: Gold and Silver and in the Nintendo DS games: HeartGold and SoulSilver.