Beth Holloway sought one thing for 18 years: answers about what happened to her missing daughter.

She got them Wednesday when Joran van der Sloot, long considered the chief suspect in her daughter's 2005 disappearance in Aruba, admitted in submitted court filings to bludgeoning Natalee Holloway to death on a beach and dragging her body out to sea.

"The never-ending nightmare is over," Beth Holloway told CBS News correspondent Janet Shamlian.  "And to me that's better than closure."

Van der Sloot, 36, pleaded guilty on Wednesday to federal charges of attempting to extort money from Beth Holloway in 2010 in exchange for information about the location of her daughter's body. The plea agreement included an unusual provision for van der Sloot to "provide all information and evidence" about what happened to Natalee Holloway and to let her family hear him in "real time" give his account to federal investigators.

Beth Holloway said in an interview with The Associated Press that the family made the decision to allow the plea agreement to "finally get the answers we've been searching for for all these years."

Natalee Holloway, 18, went missing during a high school graduation trip to Aruba with classmates. She was last seen May 30, 2005, leaving a bar with van der Sloot, a Dutch citizen and student at an international school on the Caribbean island where he grew up.

Natalee Holloway's disappearance quickly became an international sensation, filling evening newscasts with live reports from the island and photos of her smiling cherubic face. Her disappearance also spawned countless books, podcasts and movies.

"She was killed just by standing her ground"  

Under the terms of the plea agreement, Natalee Holloway's parents listened and watched several weeks ago as van der Sloot, under questioning from his own attorney, described what happened on the beach. Prosecutors filed excerpts of the conversation with the court.

He said Natalee Holloway was physically fighting his sexual advances and that he kicked her "extremely hard" in the face while she was still lying down. Van der Sloot said the teen was already unconscious, or even dead, when he picked up a nearby cinderblock and brought it down on her face.

"I smash her head in with it completely," van der Sloot said, according to an Oct. 3 transcript of the meeting.

He then said he dragged her body until he was knee-deep in the waves and pushed her out to sea.

"It's just blistering to your soul, and it hurts so deeply," Beth Holloway said of hearing the details. "But you know that you're there in a functionality role because this is the moment where I've been searching for for 18 years. Even as hard as it is to hear, it still not as torturous as the not knowing. It was time for me to know."

Beth Holloway said she recognized her feisty daughter in van der Sloot's description of her kneeing him between the legs when he refused to stop his sexual advances.

"Yes, I said, 'That's her,'" Beth Holloway recalled with a brief smile. "She fought like hell. I think she fought like hell with her killer."

"She was killed just by standing her ground," Holloway told CBS News. "I was so proud of her."

Dave Holloway, Natalee's father, called van der Sloot "evil personified" in a statement issued after the sentencing hearing.

He said that after witnessing the confession he believes van der Sloot worked alone in killing his daughter but that he suspects others may have helped dispose of the body or covered up the crime. Natalee Holloway's body was never found during land and sea searches.

"While it may not be in a court of law, I believe their judgment is still to come," Dave Holloway said. "We are living every parent's nightmare. Today and every day, please hug your children in honor and loving memory of our daughter, Natalee Ann Holloway."

Beth Holloway flew to Aruba in 2005, quickly piecing together that van der Sloot left the bar with her daughter, tracking him down and questioning him about what happened. What followed was 18 years of lies and taunts, but she believes they finally have obtained the truth, she said.

"You are a killer"

At the hearing Wednesday, Beth Holloway again stood in front of van der Sloot.

"You are a killer," she told him. "I want you to remember that every time that jail door slams."

Shackled and wearing an orange jail uniform, van der Sloot told the crowded courtroom he hopes his statement provides some closure.

"I would like the chance to apologize to the Holloway family, to my own family," he said, later adding, "I am no longer the person I was back then."

Mark White, an attorney for Dave Holloway, said he understands from law enforcement authorities that van der Sloot cannot be prosecuted in Aruba - even with his confession - because the statute of limitations has expired. The Aruba public prosecutor's office said it was not immediately clear whether van der Sloot could face murder charges on the island. The investigation into Natalee Holloway's disappearance is still open, and authorities "will follow up on any serious leads," said Ann Angela, a prosecutor's office spokesperson.

Peru agreed to temporarily extradite van der Sloot to the U.S. to face proceedings on the extortion charge. He is expected to be returned to Peru in the coming days after the settlement of the U.S. criminal case.

His 20-year sentence for extortion will run concurrently with prison time he's serving for another killing in Peru.

Van der Sloot's guilty plea in a crowded courtroom, a few miles from where Natalee Holloway attended high school, came three days before what would have been her 37th birthday. She had planned to go to medical school, her mother said.

"I fully believe now, today, she would be a doctor, married, children," Beth Holloway said.

She said she is undecided how she will spend her daughter's birthday but told CBS News that she finally has peace.

"I have peace," she said. "It felt very victorious."

In:
• Joran van der Sloot
• Natalee Holloway