During a life-threatening cataclysmic event like a major hurricane, earthquake, tornado, fire, tsunami, or other disasters, our most important goal is to save our lives but most especially our souls if we are facing imminent death.
To save our souls there are four ways to forgive mortal sins, but three of them will most likely not be available to you since during an extreme emergency you will not have time to find a priest. The normal three ways to forgive mortal sins are the Sacrament of Reconciliation (confession), Anointing of the Sick (if unable to articulate a confession i.e. coma), and adult baptism (remits all the mortal sins of your past life without having to confess them).
The fourth way to forgive mortals sins is explained in the Catholic Catechism of the Catholic Church,
“When it arises from a love by which God is loved above all else, contrition is called “perfect”. Such contrition remits venial sins; it also obtains forgiveness of mortal sins if it includes the firm resolution to have recourse to sacramental confession as soon as possible.” (1452)
Perfect contrition means being truly sorry for your sins, for love of God, and the prayer to help us articulate true sorrow for our sins is the Act of Contrition. This is the most important prayer during a life or death catastrophe because it promises heaven (purgatory is part of heaven). A good example of perfect contrition is the good thief at the cross who from his heart asks forgiveness, and Jesus says, “This very day you will be with me in paradise.” (Lk. 23:43)
In the lives of the saints there are many examples of an Act of Contrition saving souls from hell, as when a woman was grieving greatly because her husband had committed suicide. She went to speak to St. John Vianney, but the confessional line was very long. She was about to give up when John Vianney was supernaturally inspired and cried out in the midst of the people, “He is saved!” The woman did not believe, so the priest reiterated, emphasizing each word,
“I tell you he is saved. He is in Purgatory, and you must pray for him. Between the parapet of the bridge and the water he had time to make an Act of Contrition. Our Blessed Lady obtained that grace for him.” (The Cure D’Ars St. Jean-Marie-Baptiste Vianney by Abbe Francis Trochu)
Another example is St. Padre Pio when a woman inquired if her brother, who had committed suicide after financial troubles, was in purgatory. At Mass, she was unable to speak with him so she sat in church praying and in tears while Padre Pio was confessing many people. All of a sudden she was notified: “Padre Pio is calling you.” She looked at the confessional, and he was gesturing with his hand, to come to the confessional. She knelt by Padre Pio, and he said: “Don’t worry, stay calm, he is saved.”
Similarly, in the life of St. Faustina, she relates on two occasions when Jesus sends her via bilocation, to the bedside of two different dying persons who did not have access to the Sacrament of Reconciliation. She begins by praying the Divine Mercy Chaplet, and they repent and die in peace, even though before she started praying both were in agony and one was surrounded by devils. She explains, in a different passage in the diary, how this process of forgiveness and mercy occurs,
“God’s mercy sometimes touches the sinner at the last moment in a wondrous and mysterious way. Outwardly, it seems as if everything were lost, but it is not so. The soul, illumined by a ray of God’s powerful final grace, turns to God in the last moment with such a power of love that, in an instant, it receives from God forgiveness of sin and punishment, while outwardly it shows no sign either of repentance or of contrition, because souls [at that stage] no longer react to external things. Oh, how beyond comprehension is God’s mercy!” [1698]

St Faustina Holding Divine Mercy Image
St. Faustina relates that making an Act of Contrition is a key to her sanctity and a secret between her and Jesus when drawing upon His mercy and forgiveness,
“What I talk to You about, Jesus, is our secret, which creatures shall not know and Angels dare not ask about. These are secret acts of forgiveness, known only to Jesus and me; this is the mystery of His mercy, which embraces each soul separately.” [1692]
St. Faustina shares that Jesus never tires of forgiving her, and that this gives her strength and resolution to continue,
“You carry me in the bosom of Your mercy and forgive me every time that I ask Your forgiveness with a contrite heart.” [1332] “Oh, how numerous are the instances of forgiveness about which no one knows! How often You have poured into my soul courage and perseverance to go forward.” [1489]
The reason Jesus is ready to forgive our mortal sins immediately is because He, too, feels and sees our pain and suffering of being separated from Him. He loves us so, so much, that it is like a mother who is physically separated from her child and mourns not holding him. Hence, Jesus reminds St. Faustina,
“My Heart was moved by great mercy towards you, My dearest child, when I saw you torn to shreds because of the great pain you suffered in repenting for your sins…I see every abasement of your soul, and nothing escapes my attention.” [282]

(Simulated disaster)
Finally, know and trust that in a great Earth-shattering disaster when facing impending death and there is no priest available, the moment we repent from our heart and make an Act of Contrition our mortal sins are truly forgiven! It is important that we trust in His mercy (JESUS I TRUST IN YOU), and believe that He pours out many graces as He tells St. Faustina,
“Know that as often as you come to Me, humbling yourself and asking My forgiveness, I pour out a superabundance of graces on your soul, and your imperfection vanishes before My eyes, and I see only your love and your humility. You lose nothing but gain much.” [1293]
*** PLEASE NOTE: The surest way to obtain the forgiveness of mortal sins is the Sacrament of Reconciliation for Jesus, himself, makes it his first priority to the apostles after the resurrection,
“Receive the holy Spirit. Whose sins you forgive are forgiven them, and whose sins you retain are retained.” (Jn. 20:22-23)
Act of Contrition
O my God, I am heartily sorry for having offended Thee, and I detest all my sins because of thy just punishments, but most of all because they offend Thee, my God, who art all good and deserving of all my love. I firmly resolve with the help of Thy grace to sin no more and to avoid the near occasion of sin. Amen (Compendium of the Catechism of the Catholic Church)