4 different base types of Chalices. (Pthumeru Chalice, Hintertomb Chalice, Loran Chalice, Isz Chalice) 3 are from bosses you find in the normal game (all 3 bosses are optional I think and it's very easy to miss 2 of them) The last chalice is found inside a chalice dungeon I think.How do I get the other Chalices? Do the higher level dungeon chalices drop from the normal game bosses, or do I need to grind dungeons and hope another one drops like the Root one? I completed a Root P dungeon too, and didn't notice anything different than the normal one. 3 levels, fairly identical in size and mobs to the normal one. Same bosses, minus the giant. End boss was the fire dog. No new chalice though.
Once you beat a Chalice dungeon you should be rewarded with another chalice of the same type but higher depth (I think there's 5 depth levels) as well as a Root chalice of the depth you just beat. Root Chalices let you make randomized dungeons depending on the items you use to create it. I think that's how that shit works. I haven't messed around with root chalices that much so I could be wrong about that.