(CNN) -

If the name Diana Nyad sounds familiar, it's probably because you've heard of her incredible feats of human performance -- before people like Lance Armstrong and Michael Phelps became household names.

Meeting Nyad, it's instantly obvious there's something different about her. By spending just five minutes with her -- or better yet, watching the 62-year-old swim -- you'll know you're in the presence of an amazing athlete.

On Sunday, more than 30 years after her last competitive swim, she will once again take to the waters of the Straits of Florida to attempt the 103-mile swim.

It's her fourth attempt to claim what she calls the "Xtreme Dream."

"I'm feeling some pressure," she said in an interview that aired Friday. "I'm feeling tremendous inner pressure that this has got to be it, this has got to be the last time.

"On the other hand, I have to tell you, I am sky-high excited," she said. "My adrenaline is just pumping out of my skin."

In the 1970s, Nyad was unstoppable. In addition to winning multiple swimming marathons, she was one of the first women to encircle the island of Manhattan, and she holds the world's record for longest ocean swim -- 102.5 miles from the island of Bimini in the Bahamas to Jupiter, Florida.

But there was one goal that eluded her.

"I'm turning 60, and I thought, 'What have I done with my life? What haven't I done with my life,'" she said two years ago.

"I started thinking, 'You know what, Diana? You've got to get real with life's lessons; one of which is, you can't go back.'"

But a chance sighting of her own face in the rear view mirror changed her outlook completely.

"I caught my eyes, and I thought, 'Wait a second. There's one thing you actually can go back for' -- and that's the dream swim, which was Cuba to Florida."

Her first attempt was in 1978.

"I remember, I got down to the shore with my six handlers," she said. "We're looking out at a raging sea of whitecaps."

Nyad said her navigator assured her that the seas calmed down almost to the serenity of a skating pond just a few miles out. Unsure, she took his word for it and dove in.

"If you're on the Everest team that's on the penultimate climb, and a storm comes in, you don't say 'What the heck, we're going anyway," she said. "In this swim, we just said, 'What the heck, we're going anyway."

Forty-one hours and 49 minutes later, Nyad's team pulled her out of the sea -- battered, delirious, ravaged by jellyfish, and only 50 miles from where she had started. That left her almost 60 miles from her intended landing spot.

Last year, Nyad twice met a similar fate.

On her first attempt in August, an 11-hour asthma attack and shoulder pain forced Nyad out of the water about 29 hours into her swim.

Again in September, it was several stings from Atlantic box jellyfish that ended her quest.

This Sunday, for the third time in a year, Nyad will take to the seas -- departing from Havana, Cuba's, Hemingway Marina on a quest to swim for the Florida shore.

"I'm ready for this," she said this week. "We've got the right team. We've got a great weather window coming up, and I'm just picturing that Florida shore and finally getting to those Florida Keys."

"I've left no stone unturned in training," she said two years ago. "I look at the weather, I look at my team, I look at shark devices, so I'm ready."

Speaking of sharks, Nyad is attempting the swim without a physical shark cage, and she is relying on an electronic shark repellent device and a team of divers to keep them away.

Why does she continue to try?