For Unsafe Work Environment you are supposed to not kill anything during the end event. You also have to avoid pushing to get the challenge.
For Thar She Blows! , avoid all eruptions on the ground and avoid any knockbacks (Nurgloth scythe during final phase).
The challenges descriptions do not describe the criteria that needs to be fulfilled, which means these challenges could be bugged. We’ll see what Fatshark says about it.
Hope it helps! GLHF