The user becomes stronger, faster, more durable, etc. as they receives damage from their opponents, environment or by themselves. They may be empowered by physical damage, mental damage or soul damage. Lethal damage can give a (near) maximum boost on the attacks of the user of this ability.
Lucario's (Pokémon/Super Smash Bros.) Aura grows more powerful the more damaged it is.
The Rage Blaster's (Super Smash Bros. Ultimate) shots grow more powerful the more damage the wielder suffers.
Yang Xiao Long (RWBY) has this ability as her Semblance.
Yang (RWBY) has absorbed enough power from the damage she's taken to overpower Roman Torchwick's Atlesian Paladin mech.
Son Goku (Dragon Ball series) possesses Zenkai (or "Full Recovery"), a trait genetically exclusive to the Saiyan race that allows him to enhance his own strength every time he recovers from near-fatal damage.
Goku Black's (Dragon Ball Super) Full Recovery has evolved to the point that any damage he suffers, including minor wounds and pain, allows him to adapt and grow stronger.
Rubilax (Wakfu) in his unleashed form becomes larger and stronger when Grovy keeps hitting him.
Gerard Valkyrie (Bleach) can use The Miracle to turn all the damage he takes to pure power...
...regenerating his limbs stronger than they used to be...
...regrowing his entire body into an even stronger form...
...and even drastically increasing his size if he is damaged enough.
Candice's (Marchen Awakens Romance) ÄRM, Scale of Blessing summons a clock that moves its hand each time she takes damage. For twelve turns, any damage Candice receives is turned into magical power.
The Panic Attack (Team Fortress 2) is tied to the wielder’s heart rate, allowing it to shoot faster and faster at the cost of accuracy when its wielder has been injured without getting killed.