World 4-1: Ant Trooper Hill
Stamp: Ant Trooper
Inside the tunnel, you'll come a ledge swarming with Ant Troopers. Use the Cat Suit to claw your way through them and grab the stamp above.
Use a Cat Suit to scramble up the ledge immediately outside of the tunnel. There's a star up there.
When you encounter the Giant Ant Troopers, use one to bounce to the nearby warp pipe. Once you arrive at the secret area, bounce up the Ant Troopers, or alternatively, scramble up the wall with the Cat Suit to grab the star above.
When riding the Giant Ant Troopers across the long spiky path, get a good bounce near the star to reach it.
World 4-2: Piranha Creeper Creek
Enter the mystery box near the start of the tunnel. Inside, you'll get 10 seconds to bounce up some sleeping Piranha Creepers to a high ledge with a star. You can do it!
When you reach the water, descend past the Piranha Creepers to find a deep star.
Stamp: Warp Pipe
Just past said water is a Piranha Creeper that extends from a suspicious ledge. Bounce off his head to reach a hidden path with many coins and, at its end, a stamp.
As you cross the poison purple water, you'll spot a hollow green star. Hit it to spawn eight green coins. Collect them all before time runs out to earn a star.
World 4-A: Brolder Blockade
Defeat the Brolders by stunning them, then tossing them into the lava. You'll get a star for defeating them all.
World 4-3: Beep Block Skyway
Take the left path when you reach the Boomerang Bros. It's tricky, but you'll have to grab the star when the beep blocks below it are active, then jump back before they disappear.
Stamp: Double Cherry
If you have at least four Double Cherry clones by the time you reach the checkpoint, you can use the elevator platform to ascend to the stamp. Alternatively, you can scramble up the wall with a Cat Suit.
After facing the second set of Boomerang Bros., hop into the nearby warp pipe. Make sure you have a few clones with you, or you won't be able to complete the challenge inside. Inside, hit the switch and collect all the blue coins before time runs out to earn a star. You'll need clones to collect them all.
Keep at least two clones while descending the beep block slide at the level's end. It's tricky, but if you do, you can hit the dual switches at the bottom of the slope and spawn a star.
World 4-4: Big Bounce Byway
When you ascend the first big platform, you'll encounter a trio of faux trampolines. Attack them, and one of the three will become a usable trampoline. Use this to reach the high ledge with the star.
If you have a Cat Suit, you can scramble up this wall just north of the checkpoint. Use it to reach a pair of bouncy pads that will take you to a star.
Up the very next tall ledge is a mystery box. Inside is another trio of those trampoline baddies and a star on a high ledge. You have 10 seconds to stun the right one and bounce to the star. We believe in you!
Stamp: 1-Up Mushroom
This stamp is hard to miss. It's in the final stretch of the level, surrounded by Para-Biddybuds. Bounce carefully to extract your prize.
World 4-5: Spike's Lost City
At the start of the level, there will be a trio of Spikes near a wall. Use a Cat Suit to scramble up this wall, then look to its end for a stamp.
Use the warp pipe at the top of the first slope to reach a hidden area. In here, you'll have to tap all the question mark tiles while dodging attacks from four Spikes. Do so to earn a star.
Once you climb the long hill with the trio of Spikes at the top, hop to the rounded walls to your left. Use the Cat Suit to scramble up the tall one, then follow it to find another star.
When you reach the section with many tilting platforms, you'll spot this star just slightly off the main path. Carefully jump to it to finish off this course's star collection.
World 4-B: Fire Bros. Hideout #1
Take out all the Fire Bros. before time runs out to earn this.
Stamp: Angry Sprixie
Enter this tent from the map to find a stamp inside.
World 4-Special: Mystery House Mad Dash
This is another series of quick challenges. For the first one, you have to hop up several jump pads before time runs out.
For the second challenge, you have to rush past some Spiny Ant Troopers.
In challenge three, you have to run from a Giant Bullet Bill. Watch out for boxes!
Challenge four involves running a gauntlet of Spikes.
Challenge five isn't too bad. Just dash across the narrow walkway.
Hit the turbo in challenge six and keep dashing. Dash past the falling Thwomps and leap to the star.
The seventh challenge is pretty tame. Hop across the swinging platforms to your prize.
Ignore the Goombas in challenge eight and head straight for the star.
The Cat Suit Bullet Bills are a pain in challenge nine. Move quickly along the narrow walkway, and you should be able to avoid them without too much trouble.
The final challenge is, appropriately enough, the toughest. Keep moving, and time your jumps carefully to avoid the Spikes' rollers.
World 4-Castle: Lava Rock Lair
At the start of the level, stun a Brolder and toss it onto one of the two tiles. Stand on the other to make a bridge fall, giving you access to a star.
After exiting the clear pipe, enter the mystery box. Inside, you'll have 10 seconds to activate three tiles. Quickly stun the pair of Brolders and toss them onto two of the switches, then stand on the third to spawn a star.
Before moving on to the walkway, use a Cat Suit to scramble up the left side of the entryway. The second ledge up here holds a stamp.
You'll see a star floating above the lava to the left of the walkway. To get it, stun a Brolder and toss it into the star. This counts as collecting it.