Irelia, for some who may not know, is a hybrid in skills, and for her ultimate she needs AP Dammage

I Start by using my Jungle with the Cloth Armor and 5 potions, following runes and skill order.
By the time I get back, i buy boots and a Dagger, to start building, Stinger, Followed by Nashor's Tooth. Followed by Malady. This will grant you, the attack speed and ability power needed for you to hit in a sever amount with all your skills. Building Cooldown at the same time. A Gaurdian Angel is to protect you since being so squishy would probably end you on team fights, and to end a Madreds.