You know, Illaoi even tells you (in her VO) how to beat her: "MOVE!"
Seriously. The people in this game cry SO MUCH about everything. Literally every single ability of Illaoi's can be dodged or avoided by, you guessed it, moving!
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She uses Q? Side step. It has a VERY readable animation, and even shows you where it'll do damage. So, like, move!
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She hit you with W? You let her get too close. (Seriously, it gives her an AA range of Tahm for ONE ATTACK, so why not try moving?
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You got hit by E? Sidestep more, and keep minions between you (Gee, like, you know, every champion with a hook). Or, in other words, move!
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You got hit by her R? Why'd you get that close to her? If you just MOVE, you don't get hit by her!
Against a somewhat intelligent person, Illaoi has a VERY rough time. Against people who have no clue and don't want to try, but instead cry to Riot for nerfs, she does amazing. She has zero mobility, zero CC (outside of a slow that's VERY situational), zero gap closers, nothing. She has to literally walk up to you to do anything. So, if you MOVE, you never take damage from her. Hard concept, I know.
Treat her tentacles like Heimer turrets: Clear them if you can, avoid them if not. Half of Illaoi's damage comes from her tentacles smacking you, and all of her sustain depends on a tentacle hitting a champion -- if her tentacles don't hit you, guess what? You take much less damage, and she doesn't heal herself.
So, please, just shut up and actually try putting in some effort and thinking for a change -- you might just beat Illaoi then.
TL;DR: How to counter Illaoi (and she even tells you in her VO): MOVE!
Edit: By the way, did I mention to move?