Goodness gracious, Byakuren puppets are actually evil. 100+ damage per round when you're only rocking 300ish HP that is not ok ;-;
Little bit of a tip for people struggling: Normally, you can only enhance every time you make your first pass by the Youkai Village by default. However, if you invest about 10k into Warp, you can simply warp to the Hakurei shrine, back to Youkai Village, and that will reset the enhancement allowances back to 1. Bit of a pain, but lets you get higher enhancement values earlier on.
Edit: More tips!
Danmaku is actually pretty potent. You'll mostly want to use Yin-Yang Shot and Youkai Buster, but with the power count being so high and plentiful you might as well consider them your real source of ranged attacks in this game - and mercifully, one that doesn't totally hog your inventory.
When you unlock Nito Fusion's Mix Function: Two Green Teas make a Refined Green Tea, which heals a lot of health. Don't neglect to craft!
Incompetence and Misfortune Talismans are your best friends. They're plentiful, easy to use (just push use!), and can help a lot with the more nasty foes.
You can use items directly out of Preserve Gaps, no need to pull them out (they'll even still show up in the main items menu!). Make sure to put your best food, spell cards, and talismans in Preserve gaps to protect them from traps/explosions and save inventory spaces!
If you're about to die, and are completely out of options, don't forget to use a Return-to-Hakurei spell card. Your level will still go back to 1, but that way you'll get to preserve your Money, which you can invest back in town.