Test Your Strength: In Banjoland, you need to make a vehicle that is heavy enough to raise the bar and ring the Cactus. If you don't want to make a vehicle, then I would suggest using the trash can. Just wack it so its movable, and just drop it on the star and hope it rings.
BBQ Beef: In Nutty Acres, just carry any old cow to the top of the volcano, and just drop it in. A simple solution to any Summer day.
Massive Damage: In LOGBOX 720, you need to go to the brain chip in the center, and just wack all of the legs on the sides. When they all fall off, you should get it.
Great Balls of Fire: I would use Humba's Cargo Copter for this. In the Jiggoseum, grab a bowling ball, and hold it inside a flame/torch.
Floater in the Pipe: In the Test-o-Track, you need to find a soccerball floating in the air. Using a stickyball or something similar, grab it and drag it into the pipe.
Head for Heights: In Showdown Town, go to L.O.G's palace, drive behind it, and climb the red wire. Then just follow the notes, until you are at the top. Now just climb the tallest pole, and wait a moment at the top.
Ultimate combo: Go to the second portal of Terrarium of Terror, then back off the lily pad. You should find two rocket like items on the platform. Get a big vehicle with a big container and put them in it. Then go underwater and you should find a door that can be opened by pushing or the like. Swim further and you should find a place like a coral reef. In the middle there is a license plate. Get it and return to your vehicle. Put it into the container and drive to the airlock.