This one's going to be an instant recognition from anybody who's read Pokémon SS. It's not really an "if I were a gym leader" so much as "make up one", but... eh.
Name: Daisuke & Satoru
Trainer Eyes Entry: "A good relaxed strategy is key. / We fight with military precision."
Type: Multi
Items: 10x Full Restore, 10x Full Heal, 2x Max Revive
Badge: Double
Yen: 20,000
Fought: After beating the game. The game explains that they're "exchange gym leaders from a foreign, master-level League".
Notes: This is a 2v2 battle, obviously. Items can't be stolen for obvious reasons.
Pidgeot lv 100
@Scope Lens
-Adamant nature, 252 Attack/Speed EVs, 4 HP EVs
Sky Attack
Double Team
Extremespeed
Sand-Attack
Dugtrio lv 100
@Soft Sand
-Jolly nature, 252 Attack EVs, 126 Speed/Defense EVs, 4 HP EVs
Earthquake
Mud Slap
Hyper Beam
Rock Slide
Swampert lv 100
@Focus Band
-Brave nature, 252 Defense EVs, 126 Attack EVs, 126 Sp.Attack EVs, 4 HP EVs
Earthquake
Muddy Water
Surf
Body Slam
Rapidash lv 100
@King's Rock
-Docile nature, 252 Attack/Speed EVs, 4 HP EVs
Horn Attack
Bounce
Flamethrower
Stomp