Use combos to increase the super move meter in the top right corner. After it is flashing, press R1 to execute a super move.
When doing the Square(3) combo, press the buttons slowly and the third attack will be a ground piercing attack that you can follow up with an uppercut by pressing Square. If you hold Square on the third hit, Vexx will power up for a more powerful attack, and his uppercut will send him into the air.
In Dragons Reach (level 2), climb up the dragon's tail. Continue climbing until you reach the yellow poles on the slippery ground. Climb the first and jump to the others. On the last one, turn to your left and try to do a long jump to a small platform with a jump pad on it. You will be rocketed over to the plateau. Walk around it. The fly suit is on the other side. Note: The jump to the jump pad may require some adjustments on your part.
After the Talon's tutorial, when the blind guy wakes you up, jump to the column in the middle that has fire on it, but do not touch the fire. After that, arrange yourself so that you are on the left side facing the exit. Hop into the fire, and rocket yourself out to the left. Proceed towards the blue rings. You will be teleported to the red tapestry. Climb to the top of it and grab the red disk. Afterwards, jump off either side to exit the tapestry.
In the pirate ship game with the three pirates from the belly of the large beast, it is easier to not try to change the colors of the squares yourself. Instead, watch the board and let the cannonballs do the work for you.