Heal for a percentage of damage dealt with your abilities. Increases with each unique takedown.
Conqueror on Irelia allows you to use your massive mobility to take extended trades/fights and dish out massive amounts of true damage.
Triumph is an all-around solid rune choice. In 2v2s and 2v1s, the extra healing can be enough to grant you the ability to sustain and move on to the next target.
The majority of Irelia's damage comes in the form of her Auto Attacks thanks to her [W]. Alacrity grants you the opportunity for an additional 1-2 autos when the enemy is stunned with [E].
If the enemy team has a ton of CC, Legend: Tenacity may be a better choice.
WhyCoup De Grace
Coup De Grace allows Irelia to continue chipping away at her target until their life bar is fully depleted.
If you're planning to duel to the death a lot, Last Stand can be a vital option to hold your ground.
Irelia is a great proponent if abusing both the Letahlity on [Q] and auto-attacks, as well as the AMgic Pen on her [W], [E], and [R]. You're also able to keep the buff up almost permanently thanks to your natural [Q] reset.
Ravenous Hunter's mid-fight and lane sustain is excellent for trades and all-in battles where you are able to land all of your abilities.