Taimumari: Complete Edition

Following the introduction/tutorial level where you are taught the simple mechanics of the game, you will end up in the town. You will experience dialogue that the game automatically puts you in. Skip through and when finished head to the left to find the white bearded man with blue clothing.
Here you will have the option of choosing levels and saving the game.

Simply choose the level labelled "Sir Fallenstar +" and the lebel will begin. From here its quite linear:
You will experience enemies and axes swinging.
Continuing through you will have to dodge arrows and will be put into another area where you must climb to the top.
IMPORTANT: At a point throughout the platforming levels you will reach an area left of the screen with a scroll-like object.
Collect it and press Y to equip it. This will help A LOT with the boss battle.
When you reach the top, you will fight a mini boss. Kill it and enter the area that opens up.
You will begin another platforming section where there are dragons that spawn in. Simply dodge and kill as needed.
Eventually you will reach the top. And the final boss battle will begin.

Here you will simply dodge and spam RB to use your ability. If you end up dying on your first attempt like I did, no worries as you will simply respawn at the beginning of the boss battle.

A quick tip in the event you are struggling is to jump near him in between his ability use. Make sure you are holding RB and let go as you are close in mid-air. This will result in more of your stars hitting and will contribute to killing him faster.

Hope this helps!!