Snag a Cannon Box from the start and destroy the statues for some coins. The ? Blocks in the next area will expand and make some bridges, ignore the first one and kill the Madpoles. Continue swimming right underwater, avoiding the Rammerhead and Blooper.
Blast the Rock Block wall and the Blooper behind it so you can obtain Green Star #1 . Swim up to the Warp Box and the Checkpoint Flag then drop back into the water. Grab another Cannon Box if you need it then descend past the Spike Blocks, going up when you get a chance. Green Star #2 is up in this little alcove, just snag it then head all the way to the bottom.
Blast the wall and defeat the enemies then touch the Green Star Ring to spawn the eight Green Coins that must be collected to acquire Green Star #3 . The best way to collect them all is to fire some cannonballs at the coins, you might run out of time otherwise.
Speaking of time, in a small alcove along the sea floor is a Green +Clock that surely helps in getting to the end of the level in time. At the end, ignore the pipe and break the Rock Blocks so you can swim up this path to another pipe. This positions you high above the Goal Pole instead of on the ground.