Right out the gate you should notice the big difference in this level remix: water cubes and Spike Blocks fill the mine, which help and hinder respectively your escape from the swarm of Fuzzies that give chase.
Green Star #1
The ? Blocks near the start cough up a Lucky Bell, and if you use the Lucky Cat Power-Up to climb up the wall directly above these blocks, you can snag the first Green Star.
The Fuzzy swarm is slow enough that you can take a bit of time to make sure it’s safe to proceed past spike obstacles. Use the Lucky Cat Power-Up ability to climb in conjunction with the moving water blocks to avoid hazards.
Green Star #2
Rather than ground pounding the Big Block here, use the nearby Red POW Block to break it open and reveal the second Green Star.
When the mine starts scrolling horizontally to the right, get ready to deal with Spinies and floor spike traps. You have some time to react to the spike traps and leap over them, but the Lucky Cat Power-Up can make things easier.
Green Star #3
It helps to try to reach this Green Star Ring as early as possible. It lets you collect the first six Green Coins near the ring’s location well ahead of the Fuzzy swarm.
The last two require the use of a Jump Panel. Make sure that you’re lined up to collect both Green Coins in one jump!
The ? Block to the left of the Warp Box at the end of the mine is a trap, as Fuzzies will crash down on top of it. Just get to that Warp Box.