#AS A LEVEL 7 ILLAOI MAIN
In laning:
Well she'll be hitting it. She'll probably immediately hit it with the W to try to get the double tentacle hit so be wary of that.
Stand outside of the tentacle hitboxes where the tentacles commanded by her W would hit and just unload your damage onto her, since she can't do anything.
If she tries to double hit with Q, your range should be enough for you to easily sidestep it.
If she tries to ult, you can just immediately back off.
Post-laning once she has a good bit of AD or in a teamfight:
You probably can't drop the Spirit duration that long anymore since she will near instantly kill it at this point provided she either has her teammates or enough tentacles to hit it with.
QSS clears the Test of Spirit debuff to extent of memory, I'd probably invest in that, or get your frontline tank who can bodyblock her E to invest in it.
Otherwise, I'd try to immediately back off if you think/know her tentacles will do enough damage to threaten your teammates.
In a 1v1:
Unless she has enough damage to instantly kill it, I'd just ranged harass her as much as possible. If not, I'd just immediately run the fuck away.
In general (in laning especially, while near turret):
Don't immediately kill the tentacles unless Illaoi's W range is long enough to command them, for the love of god.
Doing that will just spawn another.
Leave it at 1 health and wait close to it.
That prevents another from spawning (radius thing) and if she tries to use W, you can just kill it to stop it mid-animation if necessary.