Born in Pativilca, Peru, Acuña played in local bands from the age of ten, and moved to Lima as a teenager. At the age of eighteen he joined the band of Perez Prado, and in 1965 he moved to San Juan, Puerto Rico. In 1974 Acuña moved to
Las Vegas, working with artists such as Elvis Presley and Diana Ross, and the following year he joined the jazz-fusion group Weather Report, appearing on the albums Black Market and Heavy Weather. Acuña left Weather Report in 1978, and became a session
musician in California, recording and playing live with (amongst many others) Paul McCartney, Joni Mitchell, Ella Fitzgerald, Elvis Presley, Chick Corea, Whitney Houston, Plácido Domingo, former Weather Report bandmates Wayne Shorter and Joe Zawinul,
Herbie Hancock, Carlos Santana, Antonio Carlos Jobim, Beck, Roberta Flack, U2, Al Jarreau and Marcos Witt. He can be found on recordings by musicians as culturally diverse as Lee Ritenour, Johnny Clegg, Roy Orbison, YellowJackets, Lalo Schifrin, Milton Nascimento,
Don Grusin, Dave Grusin, The Brecker Brothers, Arturo Sandoval, Paquito d'Rivera, Gonzalo Rubalcaba, Brad Mehldau, BoDeans, Paco de Lucia, John Patitucci, Sadao Watanabe, Lyle Mays, Diana Ross, Sérgio Mendes, Robbie Robertson, Jackson Browne, Bette
Midler, Jennifer Nettles, Christina Aguilera, Seal and Chris Botti.
In the 1980s Acuña also recorded and toured with the Christian jazz band Koinonia, which featured session musicians Abraham Laboriel, Justo Almario, Hadley Hockensmith, Harlan
Rogers, and Bill Maxwell. The Winans, Andraé Crouch, Madonna, He played on Willy DeVille's Crow Jane Alley album and in 1987 he teamed up with Elvis Presley's TCB Band for the Roy Orbison TV special "A Black and White Night". He played percussion on
Blondie's number one hit "The Tide Is High" and also recorded more than 300 movies under the direction of Lalo Schifrin, Dave Grusin, Michel Legrand, Bill Conti, James Horner, James Newton Howard, John Williams, Alan Silvestri, Michael Giacchino, Christopher
Beck, Maurice Jarre, Steve Jablonsky, John Powell and Heitor Pereira. In 1987, Acuña was summoned back to Perú by producer Ricardo Ghibellini to be the musical producer of Los Hijos del Sol, a supergroup of Peruvian prodigies designed to promote
Peruvian music worldwide.
He has also worked as an educator at University of California, Los Angeles, and Berklee College of Music. LAMA, Musicians Institute, USC, CSUN.