I think it’s more accurate to say that on the Cross, Death tried to kill Life, but Life killed Death. That is what sin makes us to be: a dead corpse, separate from God… but in Christ and His resurrection, we are made alive.
Please watch this:
youtube.com/watch?v=WosgwLekgn8
The view of Salvation (i.e. forgiveness of sins) presented in this video is labelled “Orthodox”, but it can be believed by Catholics too. The audio-visual setup is perfect, in my opinion.
I understand that Jesus “forgave our sins” - i.e. erased and killed them - by uniting Himself completely and totally with us: taking on a human nature, living a human life, and dying a very human death. His Divine Nature was hypostatically united with His created human nature, without any mixture or confusion. Because of this union, there is a bridge between man and God; mortality and immortality; time and eternity. That bridge is Christ.
Christ is Life Itself, and when Life Himself enters into Death - as He died on Good Friday - then Death must die. When we enter the waters of Baptism, we are on the Cross, in the Tomb, and outside the Tomb all in a few seconds. All is brought into the embrace of God the Father. The Father, the Son, and the Holy Spirit enter and dwell in us as in a home.
The Cross, the Resurrection, Baptism, the Eucharist… none of these are separable. All is one big process in life, taking light and life from Life Himself: Christ.