Easy studs
Play "The Lantern Menace" level in Free Play mode. Go to the first part, and progress from the start until you reach the point where you are facing a large Brainiac skull in a symmetrical room. On the right side is an electric field, and on the left an electric port. Switch to any character that has an electricity suit (put on infinite electricity, if desired), and fill the port on the left. This will get rid of the Brainiac tentacles on the top of the stairs, and fire should replace them. Switch to Superman, and walk in the middle of the fires. Initiate his freeze-breath to extinguish the fire and get studs for it, but the fire will immediately return. Keep extinguishing the fire with Superman to get as many studs as desired. Use any stud multiplier to make this even more effective.
Hidden doughnut locations
Search the indicted location on the listed hub planet to find a hidden doughnut:
Nok: During Loontern's second quest on Nok, you will need to defeat 20 enemies in a prison area. Search the top level of cells to find the hidden doughnut.
Ysmault: Look for a burning building on Ysmault, where the Heatwave character stud is found. There is a crack in that same building that can be smashed open with a super strong character to reveal a doughnut.
Zamaron: Teleport to Zamaron, and use a flying character. Fly over the teleporter, and go past the Star Sapphire minifig statue. Just north and a little west of the statue is a rocky hill with crystals sticking out. The rocky hill is close to the starting point for Loontern's third quest. There is a tiny donut on the top of the hill. Land and walk into it, or hit it, to collect the doughnut.
Secret 1966 Batman TV Show level
Successfully complete the game to unlock the "Same Bat-Time! Same Bat-Channel!" bonus level. Go to the Batcave's main room, and fly up to the elevator with the Bat-logo to the left of the Batcomputer. When in the trophy room, fly to the far right to reach the studio set, which looks similar to the Wayne Manor study in the 1966 Batman TV show. Switch to Batman or any character with a grapple gun. Pull the grapple point to the left of the bookcase to reveal a secret passage. Slide down the pole to start the bonus level.
Easy studs...