Crowning Moment of Awesome: Though it involves a truly aggravating sequence of Button Mashing, singlehandedly pushing back the moon and then using it to take down Mashtooth in 5 is by far the most awesome thing that Starfy has done in the entire series.
...until in the 5th game when you're trying to get that 9,999-pearl clothing item, and especially when you're trying to get all the toys from the Gashapon machine (which replaces the previous games' system of simply defeating an enemy to add it to the beastiary); the toy you get is completely random to point where it's possible to get duplicates, thus eventually forcing players to resort to "farming" (itself a subversion in which you just have to collect the pearls) in order to get all the collectibles, making this particular entry in the series an inversion of this trope.
Also, while the main game is a nice, relaxing platformer, stage 10 is Time Attack. You can't even fight the Boss until you beat a certain time goal on each stage. The boss has an extremely hard-to-dodge attack that does infinite damage.
Every New Game+ in the four games has tweaked level designs, trickier bosses and some Nintendo Hard extra levels. The True Final Boss of 3 is a pain, having 12 hard to reach weak spots, moves quickly, and has a final attack in which you must hit 12 random weak spots on a meteorite before it crushes you... and then you'll have to try defusing the exact same attack again. Oh, and you are limited to 5 HP during boss battles. Sorry, no health upgrades before the fourth game.
That One Attack: Evil's Wave MotionPuke is absurdly hard to deflect, you have to repeatedly hit the crosshairs precisely over and over again just to slow it down, should you failed one of them, all you can do is to wait for the inevitable One-Hit Kill to claim your life.