It is not sure that which fast move the Mew uses, but its DPS seems to be very high. Thr Pinsir uses Vice Grip, but it does not damage the Mew much because of the Pinsir's lower CP relative to the Mew.
Finally the attacker defeats the first defender with slight injury.
Mew vs Vaporeon (1)
The next defender is a Vaporeon and uses Water Gun. The fast move is famous for its higher DPS, but it cannot damage the Mew due to the Vaporeon's lower CP than that of the Mew as well as battle 1.
It is not sure that why the Vaporeon's water type move is not very effective against the psychic type Pokemon. Anyway, the Mew beats the Vaporeon easily.
Mew vs Vaporeon (2)
The third defender is also a Vaporeon, but it has higher CP than the last one. Its CP at 2449 is also higher than the Mew.
The attacker uses Hyper Beam, because his energy bar gets full for the last 2 battles. Hyper Beam is very high power move.
The Vaporeon uses Hydro Pump, and the Mew's HP gets decreased significantly. However, the Mew uses its fast move continuously and quickly, and finally win the battle 3 and take over the gym.
creo que mew no funciono mucho vaperoen es como un raton con un gato esta re mal asique no sabe nada de pokemon es invecil