Frantic; desperate — doing something with all one's might or in a panic, showing extreme determination or urgency.
試験に合格するために必死に勉強した。
I studied desperately to pass the exam.
火事の中で彼は必死に子供を助け出した。
He desperately rescued the child from the fire.
必死の形相で彼は助けを求めた。
With a desperate look, he begged for help.
Inevitable death — the literal meaning of certain or unavoidable death (a noun usage, somewhat literary/formal).
敵に捕らえられれば必死を免れない。
If captured by the enemy, death will be unavoidable.
その行為は必死を招く恐れがあると警告された。
He was warned that the action might lead to certain death.
In shogi (Japanese chess), '必死' is a technical term referring to a brinkmate — a situation where checkmate (or an unavoidable decisive loss) is inevitable for the opponent.
終盤で相手に必死をかけられ、局面が決まった。
In the endgame, the opponent put him in a brinkmate and the position was decided.