Instructions
Purchase 20 to 30 Ultra Balls from any PokeMart. Buy an Escape Rope if you don't have a Pokemon that knows "Dig" or "Teleport." Stock up on a few Super Potions or Full Heals. Get about 15 Max Repels if you dislike encountering wild Pokemon.
Catch a Pokemon and teach it "Waterfall" and "Surf." Teach a Pokemon Ice-type moves, such as Hail, Blizzard, Ice Beam and Ice Fang. The Pokemon should be around level 35.
Travel to Fallarbor Town and head west until you reach Route 114. Walk south until you find Meteor Falls. Enter the mountain, walk west and you will see a small body of water. Use "Surf" and travel up the waterfall using HM07.
Travel through the entrance in the wall. Go down the ladder to a lower floor. Walk north and head up the ladder. Defeat the old couple if you haven't already and head up the four small sets of stairs. Fight the Dragon Tamer, jump down the ledges and go down the ladder.
Use "Surf" and swim through the entrance in the wall. You will find a dead-end. Walk around until you encounter a Bagon. You can only encounter a Bagon within these 10 squares in "Pokemon Sapphire." Use attack moves to weaken the Bagon and throw Ultra balls at the Pokemon until you catch it.