In legal docs, obtained by TMZ, van der Sloot admits to killing Holloway in a transcript of a confession made to his attorney ... where he lays out the final minutes of her life.

Joran says he and Natalee were walking along the beach in Aruba after a late night out at a local bar. He says the two found a space on the sand, laid down, and started to kiss. Joran tells his attorney, "I start feeling her up again and she tells me no. She tells me she doesn't want me to - to feel her up. Uh, I insist. I keep feeling her up either way."

Angered by his advances, Joran says Natalee then knees him in the crotch ... and he stands up and kicks her "extremely hard" in the face and knocking her out.

In a sickening confession, van der Sloot then says he grabs a nearby cinder block and smashes her in the head with it ... "I smash her head in with it completely."

Unsure of what to do with her body, van der Sloot says he then carries her into the water, walking until he's about knee-deep and pushes her out into the water to be carried away.

As we reported, van der Sloot was in court in Alabama Wednesday where he entered a guilty plea to charges of wire fraud and extortion after telling the family he'd give up details of her death for money.

Shockingly enough, van der Sloot offered up an apology to the family Wednesday, saying he'd found religion ... but that didn't work with Holloway's mother, Beth, who said he'd always be a killer.