So Toxtricity’s form (Amped or Low Key) depends on its nature, when you use a mint to a nature required for the form, will the form change too?
No. Mints only edit the stats to make them like that nature, the nature isn't changed. So an Amped Toxtricity could have the stat bonuses associated with a Low Key nature, even if it technically has a different nature.
Source
Hope I helped!