This stage is Brolder Blockade (4-A). This complete walkthrough will provide you with a 100% video playthrough and a screenshot of where you can find all the green stars.
Game Play Walkthrough Video
Brolder Mini Boss
Any kinds of attack including claw attack, fire ball, or a simple jump will make them into balls. You can then pick them up and toss them into the lava.
Green Star 1
The Green Star is yours once you defeat the Brolders.