The achievement is not so hard if you know what "sack" does mean. That doesn't mean you have to sack the city once you've won the siege. That's about the downgrading the city into a settlement once you've got it in a peace deal: there will be a popup with 3 choices and the bottommost is that what you need.
It's real to get all 4 cities until 460 AUC, you need to win 3 or 4 wars. It might be hard to fight against all 4 Diadochi at once, so alliance with Egypt at the start could be a good idea. You can also ally with Epirus and even Thrace to make the first 2 wars easier.
1. War with Macedonia, the goal: conquer Corinth. This war starts automatically in a few months after the start of the campaign. Before the war starts, move all you armies into Megara, recruit some archers or light infantry - they will help to assault cities. Once the war starts siege and assault Corinth, then move your army to Pella and also siege it. Demand only Corinth (it's needed to avoid bad events) and Pella in the peace deal.
If Thrace is also in the war with you then you can optionally also occupy and demand it's capital.
2. War with Seleucus, goal: defend your capital province. Usually this war starts automatically when you haven't yet finished the war against Macedonia. Don't worry, your satellites will help you, just finish properly your first war and then move all your army to Syria. then conquer a strip of Euphrates lands till Babylon. Once the warscore is enough make a peace deal and raze the great ancient city into a settlement.
3. War with Egypt. This is the hardest war.. Usually Egypt starts a war with one of it's neighbour (Nabatea or Cyrenaica) and calls for your help. Refuse and you'll get ability to strike Egypt without break truce penalties. Egypt has decent army but its quality is below the Phrygian. There can be 2 tactics: land and naval.
Naval: the war goal is Alexandria. Egypt has a proper fleet, but you can put Demetrius or Antigonus (if he is still alive) as an admiral. You'll have to win Ptolemaic fleet and then embark and move your army to Egyptian capital.
Land (if you haven't invested in your fleet): the war goal is Philistia. Siege and occupy Gaza, Pelusium and then Alexandria. Take Alexandria in peace deal and raze it.
4. War with Thrace (if you haven't conquer Lysimacheia in the 1st war). The easiest war. Just get their capital and raze it.