Recruit as many teammates as you can in Amp Plains, and if you have any Gastrodon on your team already, bring them (they know Mud Bomb; it's super effective). Electrike are also helpful as they have the Lightningrod ability.
The Luxio on the left side will gang up on your partner, along with Luxray, so just let them do their thing. Bring Reviver Seeds and Heal Seeds; Luxray will confuse your partner with Swagger (it's probably the most annoying thing he can do).
If you bring other teammates in, let them attack the Luxio on the bottom. They can usually handle themselves pretty well.
You can attack the Luxio on the right side. Once they're gone, you can go help your partner with Luxray and any remaining Luxio. There's usually one Luxio that wanders off along the top and doesn't do anything, so you'll have to go catch him and attack him.
Remember, without Luxray, the Luxio are powerless. Once he's gone, you have a really good chance of winning.