Ekko vs Karthus

Throw Timewinder (Q) at a champion, then position so the device passes through them again on its way back: it expands into a slowing field, and the return hits again.

Hit with Timewinder (Q) out and back, and weave in the empowered auto from Phase Dive (E): the third hit triggers Z-Drive Resonance (passive), with bonus damage and speed.

Cast Parallel Convergence (W) where the fight will happen, then step into the sphere when it appears: you stun the enemies inside and gain a shield.

Engage, deal your damage, then cast Chronobreak (R): you return to where you were 4 seconds earlier, in stasis, and recover health based on what you lost.

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.