How to introduce a hard mode in Pokemon:

Side quests where you team up and explore different forrests and caves with your various rivals. They don't auto heal, you must talk to a traveling nurse to heal both you and your rival Pokemon.

As you gain Exp, so do your rivals Pokemon, so the more you train in one area the stronger that rival becomes. Training in different areas and different times of the day at different times of the year will change your rivals team and strategy.