Tutorial 1
Even the tutorial levels contain gems. At one point during "Tutorial 1," you'll need to make a few large jumps and then drop into an area with boulders next to a ladder. Push the boulder to the right of the ladder until it falls, crashing through the floor and exposing a secret passage. Follow the passage until you find the gem.
Tutorial 2
The exit for "Tutorial 2" sits below two platforms. Jump up to the second platform and then leap into the wall above the exit door. You'll pass through the wall and enter a secret passage. Crawl along until you find the hidden gem.
Tutorial 3
The third tutorial recommends running away from falling boulders, but ignore the advice. Instead, wait for the tumbling boulders to form a staircase. Run up the boulders and jump into the wall near the ceiling to enter another secret passage, which contains not only treasure but the hidden gem.
Tutorial 4
In "Tutorial 4," make your way to the first gap, the one that requires you to hit the dynamite from below. Once you reach the ground, jump up into the left wall below the suspended metal crate to find the gem's secret passage.
Tutorial 5
"Tutorial 5" hides its gem behind the exit door. You need to jump over the exit and then jump into the wall to the exit door's left. Follow the secret passage to the gem, but be careful. Only walk far enough to grab the gem. Taking even one extra step will send you falling all the way back to the beginning of the level. This is the last gem for the tutorial stages; "Tutorial 6" does not contain a gem.
Level 1
At the start of "Level 1," turn to your left and jump into the wall beyond the spike pit. Make sure you jump far enough to reach the wall and avoid the spikes. You'll enter the wall and fall down into a secret area. Follow the passage to find the gem.
Level 2
In "Level 2," you'll need to swim beneath murky water to find the secret area. Look for the gap with four spikes. The secret passage with the gem is in the wall to the left of those spikes. You can also find an extra life on this level if you go past the underwater crates and treasure chests.