Question

What are all the abilities that reduce damage when at max HP?

Answer 1

The first one that came to mind was Multiscale, but I double-checked on the Bulbapedia site for "Abilities that alter damage taken". There are a total two abilities which reduce damage when HP is full.

1. Multiscale: Reduces damage when HP is full. Dragonite's and Lugia's abilities only (Hidden Abilities).
2. Shadow Shield: Reduces damage when HP is full. Lunala's signature ability.

Source

Comments

Worth mentioning that Shadow Shield can't be ignored by Mold Breaker and its clones, while Multiscale can be.

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In a sense, Sturdy is another such ability (from BW onward). If a Pokemon is at full health and would take its entire health bar in damage, or more, from a single hit, the damage gets reduced to its health bar size minus 1.