During game play press pause and hold R1, L2, down and triangle then release and quickly press circle, up, square, triangle, right and down in sequence.

If it does not work keep trying and memorise circle, up, square, triangle, right, down before holding the first set of buttons, then you can do the second sequence with ease

Or you can use an AR. But if you don't have one and don't want to buy one, use the cheat above.

I must say though; using cheats doesn't give me the same feeling of achievement when I complete the game.
Also, you can miss out on important items and such by level skipping using that code, so I would advise to go through without the cheat if possible.

cheats all the way
up down left right A start, level select cheat for sonic on the megadrive