First, there are only 4 attacks being taught by the Move Tutors. 3 Old & 1 New. These attacks are also exclusive to a select group of Pokémon, BUT you cannot just offload it on the Pokémon. They need to be at a specific Happiness Level (A High One) Below are the locations and the attacks that are tutored. Click them to go to their attackdex page which contains compatibility lists:
Elemental Hyper Beams
In Route 228, this old man will teach you the elemental hyper beams; Frenzy Plant, Blast Burn & Hydro Cannon.
|Frenzy Plant||User cannot attack on the next turn.||150||90||5|
|Blast Burn||User cannot attack on the next turn.||150||90||5|
|Hydro Cannon||User cannot attack on the next turn.||150||90||5|
The attack whose name was given during a competiton is found in a house on Route 210. This old lady shall teach it to any Dragon type Pokémon, and Arceus if its holding the Dragon Plate.
|Draco Meteor||Lowers users SP.ATT two stages||140||90||5|