Psychic-type Pokemon are weak against Bug, Dark, and Ghost-type Pokemon. Dark-type Pokemon are especially useful as they are immune to Psychic moves. Psychic moves also don’t do very much damage against Steel Pokemon or other Psychic types. Here are some examples of Pokemon that are strong against Psychic-types:

• Bug: Genesect, Buzzwole, Scizor, Centiscorch, Yanmega, Hericross, Kleavor, Araquanid, Ninjask
• Dark: Yveltal, Umbreon, Absol, Zoroark, Urshifu, Houndoom, Grimmsnarl, Weavile, Dusknoir, Hoopa
• Ghost: Calyrex (Shadow Rider Form), Gengar, Dragapult, Giratina, Ceruledge, Aegislash, Dusknoir, Lunala, Necrozma

Its also worth noting that some Pokemon may have a second type, which means they may be weak against other types of damage as well.