The Jurassic Shore is the fourth event in the Animals and Friends booth of Free Play. To unlock it you'll need to play through the first three events in the area, or you'll eventually get through Adventure Mode if you play that.
Jurassic Shore is a shooting game. Plesiosaurs are the pink single-headed sea monsters that go across the bottom of the screen. They'll come in four a time, in groups, starting on the right and alternating right-left.
This one is kind of annoying, because the 25th Plesiosaur is only on the screen for a split second before you miss your chance. Get a good idea of where they enter the screen -- directly below the top of the volcanoes on each side. Once you take out a group of four, move the target over the other side. The sixth group should enter at the 30 second warning, and then the single last plesiosaur will show up on the right less than a second before the end-of-level hydra pops up. Make sure you are in the right place and just hold down the right trigger.
If you hit it the achievement should pop immediately.