For the first three times Swoop tries to smash you, stand near the edge and spin attack him. Then, when his movement speeds up, throw a bomb and spin attack him and you should be able to kill him in 4 cycles.
You need to throw bombs into the thwomp's red face. After the first throw, you can vertically throw another bomb onto his head as his damage animation finishes. With the correct timing, it will fall right into the red face again when it opens up. You need to do this 3 times in total.