Mushroom Kingdom
Box No. 1 is on a ledge in the Mushroom Kingdom Castle. Jump on Toad's head, wait until he walks near the northern door and jump onto the ledge. For Box No. 2, go downstairs in the Item Shop and speak with the mushroom man. For Box No. 3, jump on the mushroom man and ride atop him until he's standing in the bottom right corner. Jump to get the box.
Bandit's Way and Rose Town
Bounce on top of the red spinning flower in Bandit's Way to get Box No. 4. Jump toward the blue flower; you should hit the box on the way. Box No. 5 is in Rose Town's Item Shop. Hop up the crate behind the pink mushroom lady, jump onto the shelf behind the counter, walk as far left as you can go and jump again. For Box No. 6, go to the left of Rose Town's Item Shop. Jump off the head of a mushroom man next to a house with no door on the ground level, enter the building, go upstairs and jump on his bed.
Forest Maze
Walk to the left side of the screen and jump in the first section of the maze to find box No. 7. Box No. 8 is to the left of the first stump you burst out of after the underground section; jump to uncover it. Box No. 9 is below the leftmost stump in the area with seven stumps and wriggler enemies; once you fall, walk to the left of the screen and jump to reveal the box. Box No. 10 is in the rightmost stump of the seven stump area. Walk left, about midway in the area, and jump up. Box No. 11 is below the leftmost stump in the second row. Jump in the northeast corner to find the box. Find Box No. 12 right past the save spot next to the hollow stump. Jump in the right corner of the screen.
Pipe Vault, Yo'ster Isle and Booster Pass
For Box No. 13, descend the second pipe in the area with six pipes. Jump up on the long ledge and walk to the very end. Jump until the chest appears. Box No. 14 is in the same area; move slightly above Box No. 13 and jump again repeatedly. Behind the save spot in the first area of Yo'ster Isle is Box No. 15. Jump in the area above the save spot until the treasure appears. Head left in the first area of Booster Pass and jump repeatedly on the plant above the entrance to the cave to uncover Box No. 16. Box No. 17 is in the same area. Head to the right of the area and jump above the hill entrance repeatedly.
Booster Tower
Climb the stairs in the room filled with Snifit enemies and jump at the very top of the stairs for box No. 18. Box No. 19 is to the far left of the area you land in after the Whomp enemy flings you from a seesaw. Box No. 20 is in the room with orange platforms. Jump atop the box at the top and then into the air. In the bottom right corner of the same orange-platform room, jump up to find Box No. 21.
Marrymore and the Sunken Ship
Spend the night in the regular room at the Marrymore inn. Climb the bookshelf and head toward the left. Jump to reveal Box No. 22. You'll find Box No. 23 on the Sunken Ship in the room with the doppleganger Mario. Jump atop this fake Mario and jump again when you reach the middle of the back wall.
Land's End and Belome's Temple
Box No. 24 is in the very beginning of Land's End. Shoot yourself out of the cannon onto the moving platform and jump when the platform reaches the top. For Box No. 25, shoot yourself out of the cannon and onto the yellow block. Move to the right and jump up to reveal the hidden box. Box No. 26 is near the spinning flowers in Land's End. Walk to the right of the flowers, near the stationary flowers, and jump on the second flower. Box No. 27 is in toward the top right corner of the first section of Land's End's secret passage to Kero Sewers. To find Box No. 28, jump on top of the treasure box you see in Belome's Temple after you have your fortune told. Box No. 29 is in the Belome's Temple area. Go down the stairs on the right and jump in the corner.
Monstro Town and Bean Valley
Box No. 30 is Monstro Town's only hidden treasure. Find Jinx, then head for the town exit near him. Locate a bush, stand to the left of it and jump. Exit Monstro Town and enter Bean Valley for Box No. 31. Descend the rightmost pipe, walk to the bottom left corner and jump. For No. 32, beat the Piranha Plant in the right lowermost pipe, go down the pipe, walk to the leftmost corner and jump. For No. 33, defeat the Piranha Plant in the top right pipe, descend the pipe, and jump in the middle of the area between the trampoline and the stairs.
Nimbus Land
Box No. 34 is in Nimbus Land's Item Shop. Jump up onto the shelf via the boxes at the back of the shop, walk as far left as you can, and jump into the air. Box No. 35 is in the upper right corner of the room with three doors inside Nimbus Castle. Box No. 36 is in the room behind the king and queen. Spot the treasure box, jump atop of that one and jump again to reveal the hidden box. Box No. 37 is back in the room with three doors. After defeating Birdo, enter the leftmost door. Descend the stairs and jump up to find find Box No. 38. Push downward against the invisible wall at the bottom of the stairs and you'll start walking off screen. Jump up at the end of the path.
The Gate
The last box, Box No. 39, is in the gate after the room with many screws. Stand to the left of the save spot and jump.