What does 必死的决心 mean? Must-die determination?
必死 = certain death

决心 = determination

必死的决心 means "A determination so strong that you prepare to meet certain death to carry it out"

It is a 誇張詞 (exaggeration phrase). 

Similar to "誓死" (swearing on one's own life)

You can omit "的" and say "必死决心"