@Fumanstu has now completed "Deep in the Shadows" including a comedy bat fall death by me as I tried to sneak up on a Yokai. Paralysis boss was completed first time when we got there with a few hairy moments from me - I went through about 8 needles!
We also did "Wreathed in Flame" sub-mission on first location (3 x wheel demons) and "Finders, Keepers" sub-mission on second location - both using the non-ochoko cup method.
The "Finders, Keepers" one is essentially kill a Kappa which has lots of health and trains you round the level towards other mobs - including a One Eyed Yokai if you let him. It was adapted for two players though as they added an extra Kappa to kill.
Also discovered that on level completion in co-op you are time limited in hoovering up the goodies at the end. All the mobs disappear and in single player you have as long as you like to run round and loot chests etc you may have missed, in co-op it auto completes after a minute or so.