In the first dream, for example, I figured out I had to hide behind this big, craggy brown mountain to avoid his death breath. The second dream was a bit unusual in that it was more like Jurassic Park in space than a Godzilla movie. There were a whole bunch of dinosaurs loose on a space station, and for some reason this angered Gozilla a whole bunch (even though he was on Earth—in fact I don't think I actually ever interacted with him during this dream, just the dinosaurs. But the dream did get cut short, so I don't know how it would have ended).
The third dream was my favorite. Godzilla was loose in an amusement park. He especially liked terrorizing this one lookout that was in the side of the mountain to the west of the park. I of course was in this lookout at that time. Eventually I got out. At one point I was running with a big crowd away from Godzilla when I realized that the crowd was dead mead. So while they turned left to get shelter under a covered marina type of place, I went straight ahead and ducked under the fence to my right. Sure enough, Godzilla's HEAD CAME OFF OF HIS BODY and trampled the people hiding under the covered area, TURNING THEM INTO DOLLS AND STUFFED ANIMALS AS IT TOUCHED THEM. Freakin' A. That was awesome. After G-man's head rejoined his body and he went off (I think to torment the ferris wheel), I went over and examined the dolls with some other survivors.
I then wandered back to the fence behind which I had hid, and realized that I had taken a foolish chance by doing so, because it was the fence to the dinosaur pen. Yikes! Fortunately there were only two types of dinosaurs in the enclosure: some small compy-like things and miniature anklyosauruses. When the anklyosauruses spun their tails around really quickly it made two "giant" monsters rise out of the ground. They were really only about ten feet tall or so. One was a giant flower, complete with incredibly thin stem. The other looked like a giant sandshrew.

Fortunately after they burst from the ground I ducked back to the outside of the fence and there was a tree that grew invincible stars from Super Mario Bros. The dinosaur zookeeper (played in the dream by Melissa Lovejoy) told me how to shake the tree to shake them loose (which as a bonus also shook loose several 100-coin coins). They didn't make you invincible the instant you touched them. You had to smash them against your chest to activate them. So I went back inside the pen, activated a star and scrambled up the stem of the evil giant flower, destroying it. It shrank back into the ground. I was confused as to how to kill the sandshrew-looking monster, but the zookeeper demonstrated that you had to smear something appetizing on yourself (blackberries in this case) and then let it sit on you while you held its mouth closed... it all seemed a little too dangerous to me.
Unfortunatley I woke up at this point, so I'm not sure whether the zookeeper succeeded or was an absolute idiot.