Rammus vs Karthus

Engage with Powerball (Q): your speed builds while you roll, and the impact knocks back and slows enemies around your target.

Cast Defensive Ball Curl (W) when you're being hit by autos: you gain armor and magic resist, and each attack returns magic damage to its attacker.

Cast Frenzying Taunt (E) during Defensive Ball Curl (W): forced to attack you, your target takes damage with every auto.

Cast Soaring Slam (R) during Powerball (Q): enemies in the center of the area also take a knock-up, and your speed extends the leap's range.

Stay near your minions or your allies: Lay Waste (Q) deals much more damage when the blast hits only one enemy.

If you can engage, jump on him: Karthus has no dash or leap to escape.

Once he hits level 6, back instead of staying at low health: Requiem (R) hits every enemy champion wherever they are, 3 seconds after he starts channeling.

If you have a shield, a heal or invulnerability, save it for Requiem (R): it hits every enemy champion 3 seconds after he starts channeling.

Once Karthus is dead, move away: Death Defied (passive) keeps him in spirit form for a while, and he can still cast his spells.