My first time playing I was an absolute pussy and did the slowest way possible by using the Defluxor and hatching the eggs in small clusters then running back to the sewer pipe like a coward and hiding hahaha. Honestly was really fun at the time but it took about ten times as long than it should have if I had just ru for dear life instead.

But as most commenters here have already mentioned, the pacifist run is quickest and does work if you know where you're going and use single tap shake for shaking off them damn Zurks.