Noun, Noun which may take the genitive case particle 'no', Na-adjective (keiyodoshi)
desperate situation with no escape; being driven into a corner; being cornered; last extremity
Yojijukugo (four character compound)
我々は絶体絶命のピンチに追い込まれた。We were driven to the wall.
Also written 絶対絶命【ぜったいぜつめい】