Be careful of his level 2 all-ins, as he has one of the strongest level 2 bursts in the game.
It’s often a good idea to surprise a Zilean with disables and kill him before he can cast his ultimate.
You and your allies should decide if they should let a target hit by Zilean’s ultimate live until the duration is over, or just kill and let the target revive quickly.
Zileans bombs gives you some time before it explodes. If Zilean is the support, try to use the bomb to take out your own minions in order to deny the ADC. But keep the current lane pressure in mind, this might not always be the ideal action.
Zilean players dislike chars who open with a silencing ability or fear. Try to use those abilities first, then do a fast hard poke and get out of his range before he can plant his bombs or worse plant double bombs on you.