Instructions
Preparation
Stock up on Ultra Balls from the PokeMart in any town. Although these Pokeballs cost 1,200 dollars each, they double the chance of capturing a Pokemon. This will allow you to catch rare Pokemon with a lower failure rate.
Keep assorted Pokemon types in your party. Don't keep a party of all fire-type Pokemon as you may come across a rare rock-type Pokemon you can't catch because it is too powerful. Have Pokemon strong in each element to ensure successful battles against rare Pokemon.
Patrol each area in the game until you have obtained the rare Pokemon. While time consuming, all Pokemon will eventually appear in their native habitat, but it will mean doing battle with several common Pokemon until you spot a rare one.
Battle rare Pokemon until their hit-point bar is red. This will weaken them enough to capture with your Ultra Ball.
Rare Pokemon Locations
Catch Kakuna, Metapod and Pikachu in Viridian Forest and Jigglypuff, Nidoran F and Nidoran M on Route 3.
Capture Clefairy and Paras on Mt. Moon, and Abra on Route 24. You can find Dugtrio in Diglett's Cave. Find Growlithe on Route 6 or Route 8, as this Pokemon is only available in the FireRed version of the game.
Search Pokemon Tower for Haunter and Route 12 or 13 for Gloom. Pidgeotto can also be found on Route 13.
Locate Dewgong, Golbat and Golduck on Seafoam island and Machoke in the Unknown Dungeon.
Search One Island for Graveler, Persian, Rapidash, Seadra, Tangela and Tentacruel.
Safari Zone
Go to the northeast part of Hoenn, and then travel north to enter the Safari Zone.
Pay the 500 dollar entry fee and you will receive 30 Safari Balls. You can use these to capture Pokemon within the zone without engaging in combat.
Run around the Safari Zone; there are four areas to explore. In these areas are the rare Pokemon Chansey, Dragonair, Dratini, Kangaskhan, Nidorino, Parasect, Scyther, Tauros and Venomoth.
Select ̶0;Throw a Safari Ball̶1; on the battle screen. Repeat until you capture the Pokemon or it runs away. If it runs away, keep searching the area for it to reappear.