These ones should be self explanatory, pretty much explore the new zones for the first time. Here is a full map of how to get there! Have fun!
https://gamepedia.cursecdn.com/deadcells_gamepedia_en/a/a4/Biome_Map.png?version=6405c74a7ac5739779ab6e26bfae8421

One is for killing the new boss, It can be found in "The Nest". The other one is for killing it without taking damage. You can cheese this by backing up your save before the boss fight and even during it. So once you take a hit, escape, copy backup save over current one and retry until you get it.

Ahhhhhhh the cutest side kick has been added to the game along with 3 of its own achievements!
First off in order to get the blueprint for this, it can be dropped by a "Jerkshroom" who can be found only in the "Dilapidated Arboretum". The first two achievements are straight forward. Just to clarify for the mushroom boi sacrifice, After summoning him, you can press the use ability again to have him run in to a enemy and suicide bomb him. This counts as the "Bound for Hell" Achievement.

To acquire the "Pact with the Devil" Achievement, You will run in to a Alter at the end of the "Morass of the Banished". There you can sacrifice your mushroom boi, This will consume him in the process leaving you with 1 less equipment. Proceed to the boss fight! Surprise, No boss to fight and you get a new armor blueprint and achievement!

To make your momma proud and prove to the world you have manners, simply do not break any doors on the first floor!