PK is an Indian film which represents humanity's biggest problem religion and all..it's about alien who looks like human visiting earth and getting his UFO's signal remote stolen by Indian thief. His journey to find it back takes him through journey of different religions and different rituals only for him to realize that it's all a prank at big scale and there's no such thing as religion it's all fake

For this story I'll recommend some kind of event that triggers his sensitive side. Like he ruthlessly killed hundreds of people during a heist(or something similar) and while looting he found a small girl/boy 4-5 years of age..and that will trigger his sensitive side. Since your story is about ruthless gangster, sensitive side towards friends won't make obvious choice.

I think you want to know how to setup villain backstory? Well I'm not director or anything but I'll share how I make my villain work out in scripts. So what sets apart a villain from hero? Firstly you need to know difference between both of them. If someone saves earth doesn't mean he's a hero. He may have selfish intentions. So you need to differentiate between these two.

For backstory
•your hero and villain should have something in common. Loss of someone close, same goals etc. Thanos and tony had same goals, to protect.
• if both have same goals, the path shall be different.
•if both loss someone close, then use this as pivotal moment. Both lost their parents, one coped up with the grief and other couldn't..one looked to future another looked for revenge

These points will help you establish backstory.

One of my best villain is Sui Ishihara AkA the general.(take some inspiration if you want)

Sui Ishihara was a robot who got caught between human Vs robot war after he lost his parents to military, human scientist saved his life and treated major injuries. He was used to defeat robots during human extermination war 1 however after he realized that humans caused his parents death and how greedy humans are he turned against humans and started human extermination war 2(that's his past)

After he lost to Xerzes, time patroller squad SSS leader, he admitted that the time he lived with humans, it was beautiful and life itself is like sun rise and it was not great to take away the life of weak humans, however he was blinded by rage and revenge..during his final moments he admired the sun that shines upon the earth(that's his present)

After his death his exo-skeleton was used by time patrollers for Futher research and development (that's his future)

Now it's pretty basic storyline but what sets it apart are small details I haven't explained(bcz People aren't interested in these small details when you're giving a summary about backstory)