Super Bubble Bobble
Firstly, beat boss in classic mode with 2 players. Enter code at "Classic" mode title screen: Left, R, Left, Select, Left, L, Left, Select. This unlocks the harder mode of the game.
Access Bonus Levels even if you die
Enter the code at the "Classic" mode's title screen - L, R, L, R, L, R, Right, Select. Level 20 will have a door appear. Touch it, to enter the bonus round.
Shoe power-up mode in Classic version
At the title screen in the Classic version, press Select, R, L, Left, Right, R, Select, Right.
Unlock final 10 levels
To access the final ten levels, you have to collect 9 letters. To get these, kill at least 4 enemies in one Super Bubble, and collect the key icon that is dropped. Then, carry on until the boss of that zone (levels ending in 0) and kill it. Instead of dropping a giant gem, it will leave a letter. Pick up nine of these (one per boss) to ultimately finish the game.
To unlock Robolun, finish all 100 levels in the new version, and select him from the character select menu. He moves faster than Bobblun and Bubblun, but can't jump as high.
Levels 91 to 100 in New version
Collect nine letters throughout the game. You must kill at least four enemies with a single Super Bubble, then collect the key that they drop. After defeating the Boss of that group of levels, it will drop a letter instead of the big gem. You must collect a letter from every Boss in the game (nine total) to unlock the final ten levels.