Eventually, when I'm not so tired, this will be a list of how to encounter every field boss in the game. For tonight, I'll start off with how to obtain the object needed to summon the new boss
Burning Eyes Nyarlhotep.
Nyarlhotep appears in Nakano only at Fullmoon, between 0:00 and 6:00 in-game time. I'll edit this later with the coordinates at which he appears. If you defeat Burning Eyes Nyarlhotep, there is a (very small) chance that Crawling Chaos Nyarlhotep will appear immediately afterward. Crawling Chaos Nyarlhotep has a chance to drop the item needed to obtain Nyarlhotep's plugin, the Broken Pieces of a Crown. This allows you to fuse Nyarlhotep, a level 86 Vile.
To summon Nyarlhotep, you need an item called
Shining Trapezohedron. This is made by giving the Junk Collector in Souhonzan (he's the guy in the pavilion next to the Demon Snack Salesman) five pieces of
Element: Trapezohedron.
There are currently two ways to obtain Element: Trapezohedron in the game.
The first is by deconstructing certain AP items. Maximillians give 4 Element: Trapezohedron at a success rate of 72% with the Power Extractors from the magic shop. Sprite Charms give 1 Element: Trapezohedron at 72%. Obviously, this is a very expensive and ineffecient way to gain Element: Trapezohedron since these items are limited in availability.
The second way to obtain Element: Trapezohedron is to deconstruct Remains of Tokya that are found in plasma. There is only one item that gives Element: Trapezohedron, and that is the metal pipes that are found in the white plasma in Ichigaya. The only patch of plasma that they are found in is located around x24, y19 (near the exit to Ueno). These pipes give 1 Element: Trapezohedron at a success rate of about 19%.
Obviously, it's much slower to get Element: Trapezohedron from the non-AP item, but it's also cheaper and gains you materials to give to our clan weaponsmiths at the same time. However, Maximillians are going for around 75k atm, so if you can find one for cheap, it is a good source of materials and not only Element: Trapezohedron. A stack of 5 metal pipes usually yields one Element: Trapezohedron and the pipes are loot in the plasma fairly often, so getting 5 Elements through farming is not terribly difficult. That is to say, don't buy Shining Trapezohedron at the ridiculously exorbitant price of 750k per that I've seen on the tradelist. ><
I currently have enough Element: Trapezohedron to create three Shining Trapezohedron. I'm planning on fighting Nyarlhotep within the next few days so I'll update with info about the boss itself at that point. Until then, have fun, and if you have any questions or a field boss you'd like me to detail next, let me know.