Instructions
Go to Lilycove City in the east of the Hoenn region. You will bump into May outside the Department Store in the north of the city.
Beat May's first Pokemon, a Level 31 Swellow. This is a Flying-type Pokemon that is resistant to Ground-type attacks, including Mudkip's Mud-Slap, so use Water Gun or an Ice-type move if you have learned one. Or swap in an Electric, Ice or Rock-type Pokemon because Swellow is weak against these attacks.
Use Mudkip's Water Gun and Mud-Slap moves to defeat May's next Pokemon, a Level 32 Numel. Numel is a Fire/Ground-type Pokemon that is weak against Ground-type attacks and extremely weak against Water-types. Mudkip's Water Gun should beat it in two or three turns.
Bring in a different Pokemon from your party to battle May's next Pokemon, a Level 32 Wailmer. This is a Water-type Pokemon, the same type as Mudkip, so it is resistant to Water-type attacks. Use an Electric or Grass-type to beat it more easily. If you're fighting just with Mudkip, keep using Ground and Normal-type moves or any Grass-types you may have learned through a Technical Machine.
Use any Ice or Fire-type attacks you have to beat Grovyle, May's final Pokemon. It is at Level 34 and is a Grass-type, which means it is resistant against both Water and Ground attacks. Use a Fire, Bug, Poison or Flying-type Pokemon, or persist with Normal and Ice-type moves if you're fighting just with Mudkip.