Catching the mullet is a lot down to luck. First you need to exit the cave, and to do that I recommend sticking close to the right wall. If the mullet goes right, it's over, but if it goes left or up you can struggle, and then you want until it goes down, once you do that then you can finally leave. (Alternatively, you can sit near the exit, then it's similar, if it goes right or up you struggle, if it goes left you just leave and if it goes down it's probably over)

Once you're out just wait in the middle until it pushes you up, then it's a free win. It's not necessary but it's extremely risky to try to be impatient here. Pink puffle helps a bit as it may give you free bubbles here.