Certified Illaoi player here. A few general tips against lady tentacles.
-DON'T FIGHT NEAR THE TENTACLES.
-Illaoi is strong in areas she had time to setup. Bait her away from the zones, or simply wipe out the tentacles beforehand. THEN FIGHT HER.
-Bait her ultimate. The range on her idol slam is really short. Nothing is stopping you from walking away and re-engaging 10 seconds later.
-If your spirit is broken, don't engage Illaoi, its asking to die. Instead wait it out or kill the tentacles to end it.
Also ranged top laners are the biggest middle finger to her in lane. Since they can safely wipe out the tentacles without effort, and never have to worry about her getting close.
In short, Illaoi is strong in areas where she has under control. Avoid fighting her in tentacle heavy areas. Be smart about your engages against her and you'll be fine. DON'T BLINDLY RUSH HER.