It's found right after you acquire the Phase Mask and ride the lift. Continue around the next corner to see the Hidden Gem in a small compartment in the wall-this was previously covered by a door that retracted after you hit the metal crate. Carefully drop down and spin into it, then double jump back up onto the ledge. At the end of the grind rail, you'll see a metal crate with an exclamation point in a little alcove under the checkpoint. Jump up there, then bounce off the boxes to reach the gem on the ledge above. There's a ledge to the top left that's hard to spot, but you can reach it with a sliding high jump from the highest phase platform.
Proceed until you have to phase up a series of vertical platforms. This Hidden Gem is found at the end of the level. When the chase starts, stick to the left side of the screen to grab it. This one's easy to spot-it's found when you start running from the giant monster. Instead of crawling the whole way, stop under the tent and jump up to collect the Hidden Gem inside.
Shortly after grinding on the vine, you'll have to crawl under a tent. Here are all the standard gems you can collect in the game. Some are pretty easy to spot, while others are quite difficult to obtain.
Every level in Crash 4 has its own Hidden Gem, so there are a lot to collect.