The former footballer's daughter died from a rare form of leukaemia in April 2021, aged just eight months old.
Cain, who is one of the recruits in Channel 4's reality series that puts celebrities through a simulation of the gruelling SAS selection regime, is brought in by directing staff in this week's episode to discuss his difficulties controlling his aggression.
He shares: "I'm in a bit of a transitional period in my life," before having to stop to gather his thoughts.
The 32-year-old continues: "I'm a family man, always been a family man, that's what I'm about. I started my own family, had a beautiful little baby girl.
"Two months into my daughter being born, we found out she had a really aggressive form of leukaemia.
"She was incredible. She showed strength, she showed courage, she showed everything it takes for a person to get on in this world.
"Then she sadly lost her life on 24 April. She passed away in my arms and it's a moment I'll never forget."
As the directing staff encourage him to open up, Cain says: "One thing I always will remember is every single day when my daughter was fighting this disease, she smiled every day, she fought every day and she made the most of every single day. That's a lesson that I'll take on to my life.
"She didn't have the chance at life that I've got, that we've got, and I definitely don't want to waste mine. I want to make her proud and I want to show people that no matter what you go through in life, you can overcome anything."
Cain is also shown speaking emotionally to camera about the traumatic time he and Azaylia's mother Safiyya Vorajee have been through.
He says: "When they told us there was nothing more that they could do, it broke me. All I wanted to know at that point was that she would go in my arms, she would go peacefully.
"At eight months old, she passed away in my and my partner's arms and I believe she had a peaceful transition to the other side."
Celebrity SAS: Who Dares Wins air on Sunday at 9pm on Channel 4.