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Hard mode v1:
Level cap = Average level of next gym's Pokemon.
Team cap = Number of Pokemon in the next gym leader's team.
Hard mode v2:
Hard mode v1 +
Field effects = Same as Reborn's. Generally gives a boost to the gym leader's type but can potentially be changed, destroyed, or even abused by the player.
Pokemon variety = No particularly powerful Pokemon available early on. If your team starts to get powercreeped later on, catch new Pokemon.
Hard mode v3 AKA Hard mode the easy way:
Damage taken x1.5
Damage dealt x0.75