Essentially, Story Mode consists of 7 minigames repeated over and over. Losing a minigame three times allows you to skip it and play the next one. Sometimes it's faster to intentionally lose, other times it's faster to intentionally win.

• It's faster to lose the snails minigame by running into the falling goop and losing.
• It's faster to win the fish minigame. You need to be a bit skilled at it and avoid mistakes, but generally just juggling multiple fish over and over seems to rack up points quickly. The closer you are to the end, the less time you save (you go from 2 minutes down to 20 seconds).
• It's faster to win the first sorting minigame only. By getting a high combo, you can easily save five minutes over losing. For some reason, it's slower for every other stage.
• It's faster to lose the puzzle minigame by holding L or R and clogging up the celery stalk. You may need to rotate the veggies so that you don't accidentally get combos.
• It's faster to win some of the cooking minigames. You have to play well in order to get the timesave (timesave gets lower every time).
• It's faster to win the slicing minigame, if you're good. Timesave is small (around 45-60 seconds, and gets lower every time).
• It's faster to win the garnishing minigame, but the timesave is so small and requires you to be so skilled, that it's probably safer to just lose.
• You can spam both the A button and the touchscreen to get through menus and cutscenes faster.