Team Athenodoros:

Typhon (Colour Change, Shell Armour, Hydration)
HP: 94
Energy: 45
Speed: 51
Stat Boosts: -1 Def
Status: Is now a Fighting type. 20% paralysed
Actions: Ice Beam => Psychic => Ice Beam/Signal Beam (If Bayleaf survived the first action)

Hephaestus (Torrent)
HP: 82
Energy: 73
Speed: 50
Stat Boosts: None
Status: 20% paralysis.
Actions: Brick Break => Grass Knot => Grass Knot
Add Ice Beams at the start until Bayleaf falls.
Team Banryu:

Espio (Water Absorb)
HP: 72
Energy: 73
Speed: 40
Stat Boosts: None
Status: Is now a Fighting-type. Sleeping for 3 actions.
Actions: Shadow Sneak x3 @ Lapras

Agrith (Overgrow)
HP: 11
Energy: 43
Speed: 60
Stat Boosts: None
Status: Sleeping for one action
Actions: Solarbeam prinplup > aromatherapy > magical leaf > prinplup (in this order AFTER wakeage)
Light Screen for 3 actions. Sunny Day for 4 rounds.
Turn order: Agrith >>> Espio >>> Typhon >>> Hephaestus
Action 1:
Espio and Agrith nap, as Typhon charges an Ice Beam, finishing her off for the match. Heph decides to Brick Break Espio, but to no avail, as his muscles seize up!
Action 2:
Typhon and Hephaestus continue their assault this action, as Typhon blasts the sleeping Espio with powerful Psychic energy, but it seems to do surprisingly little, despite the super effective attack. Thank God for Light Screen! Unfortunately, the Heph remains paralysed.
Action 3:
This time, it's Typhon's muscles that seize up, and he's unable to launch his Ice Beam. Hephaestus is free to attack, however, and he uses the tree roots in the clearing to trip Espio and slam him to the ground. He finally wakes up though, as the Light Screen fades.
Calcs:
Team Athenodoros:

Typhon (Colour Change, Shell Armour, Hydration)
HP: 94
Energy: 38
Speed: 51
Stat Boosts: -1 Def
Status: Is now a Fighting type. 15% paralysed

Hephaestus (Torrent)
HP: 82
Energy: 67
Speed: 50
Stat Boosts: None
Status: 15% paralysis.
Team Banryu:

Espio (Water Absorb)
HP: 62
Energy: 73
Speed: 40
Stat Boosts: None
Status: Is now a Fighting-type.

Agrith (Overgrow)
HP: KO
Sunny Day for 3 rounds.
Athenodoros, order please.