Hello, i used to be Diamond 3 or something playing only zac, which is why he's the only champion i know how to play properly. I would therefore like to share my very specific knowledge on this champion :--)

Most people don't really like to focus on ability haste on zac as they're afraid of not being tanky enough.
There are two reasons why i think ability haste is great: it makes you a snowballing monster, and it's a lot more fun to play.

Since writing is hard, here's a list of reasons why ability haste is so great on zac:
More Ability Haste = faster clearing, faster map movement, more healing, better objective control, more blobs for spamming Unstable Matter, more damage and movement in teamfights and so on ...
And also, since zac can revive himself with his passive Cell Division, he can play more aggressively without dying.

Because your map movement and farming is so effective, you'll be able to stay in front of your enemies in XP and gold, which means that you'll be tanky without the need to sacrifice ability haste for tankier items.
Your map control will also be a lot better as you can move around the map fast and easily escape if you go too deep.

Here are some neat little ways to use zac's abilities in ways which may not seem very obvious:

• Increase Elastic Slingshot CC duration: If you charge Elastic Slingshot for at least 1 second, the duration of the knockup is doubled from 0.5s to 1s.
  
  
• Use other abilities during Stretching Strikes: You can start channeling Elastic Slingshot at the moment you grab your second enemy with Stretching Strikes. This means that you can charge Elastic Slingshot for 1s before the CC from Stretching Strikes is completed if you time it right.
  
  
• Instant Elastic Slingshot (obvious, but really useful): If you tap Elastic Slingshot on top of you, you can instantly CC enemies without giving them time to react.

The most powerful zac combo imo:

• Stretching Strikes- Flash combo: use Stretching Strikes on an enemy (champ, minion, ward,...) then flash-grab another enemy. This means that if you're in flash range of a key target, you can CC them without giving them time to react.
  Once you do this you can follow up with an instant Elastic Slingshot (or channeled Elastic Slingshot for 1s for longer CC) and Let's Bounce! to lock the target down. This can be a game-changer if you know who to target.