How to Get Suicune on Pokemon Fire Red

Go to a Pokemon Mart and buy a lot of "Max Repels" and "Ultra Balls" (the more you have, the easier this will be).

Go to any Pokemon Center and make sure you have a Pokemon in your party between levels 45 and 50 with the move "Mean Look." When you encounter Suicune, it's going to try to run. "Mean Look" prevents it from running. Put this Pokemon at the start of your party so it's the first to go into battle.

Go to the grass patch on Route 2 near the Viridian Forest to begin your hunt for Suicune. While you can literally hunt for the Pokemon anywhere in Kanto, many players recommend Route 2 since you need to frequently leave the area in order to make Suicune appear. Save your game before beginning the hunt.

Use a "Max Repel" and run in the grass for roughly 25 steps. If Suicune doesn't appear, enter the building to your north and exit immediately. Repeat this process as many times as necessary. Each time the effects of your "Max Repel" wear off, use another.

Use "Mean Look" immediately when you encounter Suicune. This prevents it from fleeing so you can actually battle it and catch it. If you're willing to use your "Master Ball," use that instead of "Mean Look" to catch Suicune immediately without the trouble of a battle.

Weaken Suicune using attack moves, but don't kill it. Instead, lower its health bar as low as possible or until it's in the red. If your Pokemon has a move to put Suicune to sleep or inflict paralysis, use it.

Throw "Ultra Balls" at Suicune. It may break free several times before you actually catch it, but if you lower its health enough and put it to sleep or paralyze it, you'll eventually get it.