This was one of my favourite childhood games, and I still play my cartridge from time to time. It's relatively easy to see that certain power-ups are recurring in certain levels. What I don't know is whether any power-up can occur in any level, but I've been able to get the speed shoes in the very first level. (Whether a 1- or 2-player game makes any difference here, I wouldn't know either.)
My guess is that obtaining the power-ups he does was not a calculated effort.
Edit:
The type of umbrella that appears can be manipulated. There is a blue that allows you to skip 3 levels, and a red that skips 5. (The arcade version also had an umbrella that skipped 7 levels. Differences between games are listed in a
Special Items FAQ for the arcade version, that is hosted at GameFAQs.)
The exact numbers and other statistics should be in the FAQ. Seems you can affect the appearance of many things in the arcade game, so if this is carried over intact, you could easily get your way. Speed shoes and candy are the most relevant here, but most things have variables, apparently.
Umbrellas appear throughout the game, and since every one potentially skips 5 levels, they will be worth waiting for. I think you need to get 20 water bubbles all in all for the 5-level umbrella to appear, so that should easily save time, if it can be affected to this result. Save a few water bubble to skip time-consuming levels, unless umbrellas stop appearing at some point.
BSulpher's FAQ has information about "bubble-turned-items", and map layouts, so that is a good read. (Fun to turn bubbles into goodies as often as possible.)
I also watched the movie again, and realised how much it bothers me when he doesn't attempt to get all the fruit and other extras. But what's actually detrimental is how he doesn't obtain the speed shoes until level 16 for player 2, and some 10 levels later for player 1. There is time to be saved there.
Most levels would not benefit from the use of destruction power-ups, since they take time to appear, and the item activation animation can be slow. The one he used in the movie was one of the better ones, but I'm not sure it ultimately saves time compared to the conventional method with 2 players.
Andreas