The walkthrough will be useful but let's go over the main points of this stage. :)
Your main enemies will be club oni that break out of the statues that dot the area and mysterious staff-wielding oni that come out in a puff of mist. Later a few katana-wielding oni (one of which will be the midboss) will make life more interesting.
Remember that once an enemy flashes that means you can grapple kill it with RT. In fact, be sure to grapple kill a katana oni to get a sword artifact from it. A cicada artifact will be around the clearing where the bell is. And a coin artifact (which will net you a hidden artifact achievement) will be found in the last area upstream across from the temple.
Main puzzle strategies are to light various "lanterns", floating rocks on stands with a band of glowing light across each of them. The hole at the top needs to be lit and the best way to do it is by grabbing and equipping fire bullets from the fireflies flitting around the stone garden lamps. Then shooting the floating lanterns to light them.
Use right stick to target the lantern and once fixed you'll know you can shoot accurately.
The other method is to grapple kill a staff oni with a lantern of its own. And RT it against the floating lanterns to light them. You'll see this oni lantern in the beginning of the stage. I think that's the only place where you'll have to use the oni lantern.
Midboss fight. Once you ring the bell, a katana oni will appear. After the cutscene, hit the oni a couple of times and jump back to give it time to rush past you with its sword thrust. Then rinse and repeat until it flashes. Do a grapple kill (RT) and follow the directions. IMPORTANT: Don't press any buttons until the directions appear or you won't finish the kill properly and won't get the sword artifact. Since you'll meet more katana oni later, I'm imagining you will have other chances. But this midboss fight is the best guarantee. If you don't get the artifact, immediately quit and continue again to reload at the midboss cutscene and do the fight over.
For the final boss, the big ape, you actually don't have to fight the ape, only lure it to its own doom. The objectives aren't clear here, only saying "clear the temple." What it means is to have the ape or you knock down all the pillars supporting the temple floors and ceilings. There will be a total of 3-4 floors, each successful clear will earn you a quick cutscene of you being smashed down to the floor below. Staying clear of the ape overall will keep your health up (remember, your health regenerates after a period of no combat). Once you "clear the temple", the temple will take care of the ape for you, and you will have passed the stage. Congrats!