Here is the full list of all 16 King Kaiju achievements.
Toss a person up in the air and catch it in your mouth
Eat 50 trees
Crush 25 dumpsters with your grip
Beat a level as Megacat
Build up a combo of destruction totaling at least $25,000
Catch hold of the helicopter holding the score display
Enjoy the beautiful day by eating some ice cream
Squeeze a large building chunk with your grip
Balance a building so that it can have nice scenic view of the city
Beat Level 3
Grab a plane in each hand.
Beat Level 2
Throw a car high up into the air to make your own fireworks
Beat Level 1
Squish a person by throwing a car at them
Take down a news copter