For the vast majority of levels, you can get most but not all of the Prize Bubbles in a single playthrough of a level. For the remaining Prize Bubbles, you will need to use other human players (local or online), extra controllers and/or an exploit involving controller assignment.
Prize Bubbles are worth five times as much as Score Bubbles, but they only count as one bubble for the purpose of mulipliers.
Any Prize Bubbles collected during a level remain collected, even if you have to restart or exit the level before completing it. However, you will not be awarded any gold Medals or any corresponding Gifts until you step onto that level's Scoreboard.
Score multipliers can affect more than the bubbles you picked up to get the multiplier; they modify the score of every Score and Prize Bubble since your previous multiplier. For example, let's say you picked up 200 points without getting any multipliers. Then, you collect five Score Bubbles and get an x2 multiplier. Instead of getting 200+(50x2) points, you actually get (200+50)x2 points. This can be used to your advantage if you care about getting a high score.
Check behind objects if they are not in the background layer! A number of Prize Bubbles are hidden there throughout the game.
Unlike many platforming games, you don't really have to worry about enemies. Most enemies you encounter can be destroyed by simple Goomba Stomping. What you really have to worry about are environmental hazards like spikes, electricity, fire, horrible gas, explosives, et cetera.
Touching spikes, horrible gas or electricity is always a one-hit kill. Explosives and fire are more lenient. If a player is close but not too close to an explosive, they'll be covered in soot but be otherwise unharmed. If a player only touches fire once before landing on safe ground again, they'll be singed but safe.
When a player joins the level or turns their controller back on, they will spawn at a nearby activated Checkpoint without exhausting one of the lives.
While the lives given by Checkpoints when playing solo seem generous, they are much more restrictive when playing with multiple people since the same number of lives are shared between every player. (This is especially evident on some Cooperative Challenge areas, where it often feels like you have way too few lives rather than too many.) So, I recommend that you avoid killing your fellow players for laughs, as it hurts everyone (including you) rather than just them.
Assuming the Checkpoint has some lives remaining, you can activate an Checkpoint earlier in the level to give you more lives to exhaust. This can be useful for Cooperative Challenge areas.
Assuming the Checkpoint has sufficient extra lives, sometimes it's advantageous to simply pop via the Retry option and respawn at a Checkpoint activated by another player further ahead to save time and bypass obstacles.
When competing in a race, slapping someone forward is not advantageous as the slapped player gets up before the slapping playing finishes their animation (where they can't move), which only serves to put the slapping player behind.
If playing with other people, any collected Prize Bubbles are awarded to all players rather than just the player who specifically collected it. This is particularly useful in Cooperative Challenge areas, where one person can (or may have to) collect the bubbles but reward everyone.
It's possible to play through levels in areas that don't have access to yet when playing with other people who do have access, and you can even keep the collected prizes (as well as sometimes unlocking the level before you are "supposed" to).
Players can hold or hang on to other players. This is useful for moving many players when a Grab Switch needs to be activated to raise or lower a winch, but it generally isn't useful when trying to swing because the extra weight might not allow the swinging object to reach its maximum displacement.
You can use your Popit Menu for more than Retrying or changing your Costume while playing a level. If you'd like, you can manipulate Stickers and Decorations with your Popit Cursor. You can even take Stickers or Decorations from the level and place them on your character! This is one of the only ways to get some items (like the Hammer & Sickle Sticker in "The Wilderness") that are otherwise inaccessible.