You get the elemental punches by move tutors.
D/P: None
Pt: Route 212 Move Tutor
HG/SS: Battle Frontier Move Tutor
FR/LG: None
R/S/E: None
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Thunder Punch, Fire Punch, Outrage, and either Fly or Ice Punch.
Of all unfortunate things you can't get ice punch or fire punch or thunder punch, all of the punches must be learned by a Pokemon that can by level.
Fighting/Pshychic Pokemon can learn it. Medicham learns them.
Hitmonlee is more defencive and Hitmonchan is high in attack. Hitmonchan also learns and the punches: ice punch, fire punch, and thunder punch
lets see. well first you need a medicham teach it Meditate fire/ice punch NOT thunder punch doesn't matter didn't you read the above!