During gameplay access the Team Menu. Then, hold down Select, press the Left Analog-stick Up and rotate it three times clockwise. Immediately rotate it counter-clockwise three times (you should've held select the whole time). Now a new icon should appear under the log icon in the lower right corner of the screen. Click it to access the cheat menu, which should contain options for all weapons, invincibility, unlimited weapon energy, level skip, and level selection.
Thanks to Revolution readers Kasper Nyboe and F-Force!