As far as I can tell, upgrading your level has no effect on the game apart from changing the music and your trail, does it affect your score and do I need it to get the bonus stages?
During levels, the player obtains power-ups that upgrade the score multiplier, starting at 'Hyper' and progressing through 'Mega', 'Super', 'Ultra', and finally 'Extra'. As these multipliers are gained, the background music becomes more advanced accordingly, with new melodies being added and modern instrumentation layered on top. Commander Video is also able to collect gold bars distributed through the course of the levels - if all the gold bars in a level are acquired, the player is given access to a short bonus stage based on Pitfall, the famous Atari 2600 game programmed by David Crane.
Basically, the "extra" stage is just the highest multiplier you can get for your score and it doesn't affect whether you get the retro bonus challenge at the end of the level.
Getting this multiplier is part of what you have to do to get "Perfect" on a stage:
- reach the Extra multiplier
- collect all gold in the main level as well as the bonus challenge level
- perform all the possible score-awarding actions (such as jumping on springboards) even if they're not necessary to complete a level.
In the Steam version of the game, you also get an achievement for reaching Extra and for getting PERFECT!! on a challenge.
Upgrading your level gives you points and increases your multiplier.
If you don't upgrade your multiplier, you won't be able to achieve a "Perfect!!" on that level.
(And you'll immediately fail the level if you're playing on Perfect difficulty).