Please be advised that this page of the walkthrough contains spoilers.
Below is a list of every 'secret room' in the game, in order. Each secret room will become unavailable given the progression of the plot.
First Cave. Lure the critter on the top right down towards the door back to the Start Point. Hop on top of it just as it begins to jump and you'll stay on its head - then quickly jump up to the ledge above. Jump into the bat as it swoops down and hold your jump button and the left direction, and you should squeeze into the gap.
Reservoir. Make a running jump into the pool, and as soon as you land, jump again immediately. If done correctly, your horizontal momentum will stay the same. Do this at least twice, and you should have enough time on your AIR meter to reach the door to the Chimney.
Sand Zone. Set the 'Mimiga' and 'Flower' teleporters to one another, then climb out of the pit where 'Flower"s teleporter is by using the beetles as stepping stones to get out. Once out, use the 'Gaudi' teleporter, and make your way to Misery's Abode.
Sand Zone. After returning from the labyrinth, head back to the 'Labyrinth' teleporter, then use the ●DOG WHISTLE●. The teleporter should reset, leaving you trapped there, but the teleporter will remain active...
Plantation. Give Balrog back Curly's ●MACHINE GUN● if you took it, then beat the Last Cave, etc. After you get control of Curly, level the ●MACHINE GUN● up to Lv3 and use it to propel yourself up Plantation, to a door that was previously locked. Head inside.