Phase 1: Preperation
1. Recruit an Eliectrike
2. Recruit a Ground-type pokemon
3. Have many Oran Berries and Reviver Seeds on hand
4. Make sure you bring a Vile Seed
5. Teach your leader Vaccum Cut
Phase 2: Battle
1. Use Vaccum Cut at the start of the battle before the enemy closes in
2. Throw the Vile Seed at Luxray to destroy his defenses
3. Continue to use Vaccum Cut until the Luxio are defeated
4. Focus your energy on the weakened Luxray
5. Claim your reward
How's that?