Level 1-2
The first and only chest for this level is in plain site on top of the ledge about halfway through the level.
Level 1-3
The first chest you will need the animal ability to get. Just dig through the dirt to get to it. The second chest is impossible not to get. It's inbetween the two ledges.
Level 1-4
The first chest is in the room with the star blocks on the ceiling. Just break them and climb through. The second chest is after the lollipop in-between the two rows of spikes. The third chest is right above your head after the lollipop room.
Level 1-5
Just fly all the way to the top of the area with all the barrels to get the only chest of the level.
Level 1-Extra
The first chest is in the room with the hi-jump enemy. Get the hi-jump ability and fly up the room until you get to a split. Go up the right side of the room and go inside the door to find a treasure chest. The second chest is on a floating platform. Its not hard to get at all.