The Pokémon type that can beat Psychic-type Pokémon would include Bug-type Pokémon such as Pinsir, Pineco, Illumise and Volbeat, Ghost-types such as Misdreavus, Shuppet, Dusclops, Banette, Dusknoir and Duskull and Dark-types such as Umbreon, Absol, Mightyena, Poochyena, Liepard, Arceus, Purrloin and Darkrai.
Dark and ghost type Pokémon.
Hypno doesn't evolve.
Grass, Flying and Rock types.
Electric
Gastly has hypnosis as soon as you catch it also drowzee, hypno and many other ghost type Pokemon and psychic type Pokemon.
Fighting and Fairy
Hypno is #97 in the national pokedex, and it is a Psychic type Pokemon.
flying
Hypno doesn't evolve.
Grass, Flying and Rock types.
Electric
You'll need to evolve Drowzee to get Hypno.
rock
Gastly has hypnosis as soon as you catch it also drowzee, hypno and many other ghost type Pokemon and psychic type Pokemon.
ground
Fighting and Fairy
Bug, Ground, Psychic, and steel
Hypno