Irelia vs Jax

Mark your targets with Flawless Duet (E) or Vanguard's Edge (R) before Bladesurge (Q): if the target is Unsteady or dies to it, its cooldown resets.

Before a trade, hit minions with Bladesurge (Q) to stack Ionian Fervor (passive): each stack gives attack speed, and at max stacks your autos hit harder.

Place the two blades of Flawless Duet (E) on either side of your target: only enemies caught between them are stunned.

Use Defiant Dance (W) to absorb a burst: you take less damage while charging, and the longer you hold it, the harder the release hits.

Take a short trade, then back off: Relentless Assault (passive) increases his attack speed with each consecutive auto.

During Counter Strike (E), back off instead of attacking: he dodges your autos, then stuns nearby enemies, dealing more damage per dodged auto.

Trade right after Counter Strike (E): it's both his defense and his only stun, and it has a 17 to 9 second cooldown.

In the late game, don't leave his split push unanswered: send someone to hold his lane, or force an objective on the other side of the map.