Zac’s goos can be crushed by stepping on them, denying him health regeneration.
Zac’s passive blobs can be smited. Kill them fast so that he won’t be able to revive.
Zac can be interrupted while casting his Elastic Slingshot.
If he activates his ultimate, even if you stun him it will still be activated.
Zac’s blobs act like minion spawns and are susceptible to certain effects such as Volibear’s roar fear and, most devastatingly, Syndra being able to pick a blob up, hold it for as long as possible, then toss it away or into turret.