Ezreal vs Karthus

Land Mystic Shot (Q) as often as you can: each hit lowers all your cooldowns and adds a Rising Spell Force (passive) stack.

Detonate Essence Flux (W) with a spell rather than an auto: the orb deals its damage either way, but a spell refunds its mana cost plus a bonus.

Save Arcane Shift (E) to escape unless the kill is certain: it's your only way to reposition, on a 26 to 14 second cooldown.

Cast Trueshot Barrage (R) across the map to finish a fleeing target: it hits everything in its line, but deals less to minions and non-epic monsters.

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.