From 1984 to 1986 he studied composition and music theory with Prof. Gerhard Lisken and piano with Heidi Kommerell. In 1986 he finished school and won the 1st prize at the "Forum of Young German Composers".
In 1988 he began to study instrumental composition under Prof. Nicolaus A. Huber and electronic composition under Prof. Dirk Reith at the Folkwang University in Essen, Germany where he passed his Finals in composition in 1994.
In 1990 he received first prize in a composition competition run by the Cooperativa Neue Musik and the Felix Mendelsohn Bartholdy Award for his string quartet "Nächte zwischen den Gezeiten". 1991 he won the first prize in the National Competition of German Music Academies with "Ambito" for french horn and in 1993 he received the Folkwang University Prize. Until 1996 Achim Bornhoeft worked with the choreographers Olimpia Scardi ("Cabotina"), Stefan Hilterhaus ("Floot", "invar") and Wanda Golonka ("Gegnung").
Their productions appeared at various theaters in Germany and other European countries. After grduating in composition he received a DAAD scholarship for the Computer Center for Research in Music and Acoustics (CCRMA) at Stanford University. Between 1996 and 2005 Achim Bornhoeft has been a lecturer at the Folkwang Academy and the Universities of Duisburg and Tuebingen. 1998 he received the one-year composers scholarship from the Heinrich-Strobel-Stiftung and produced several full-length choreographies ("Lumen B", "Ellis Is." "Thin as pain") with his own company.
In 2001 he was artist in residence at the Center for Art and Media (ZKM) in Karlsruhe, Germany where he founded the SUMTONE label together with the composers Michael Edwards and Ludger Bruemmer. As a visual artist he got the Arts Fellowship for his sound sculpture "Orplid und Schilf" at the Mummelsee, Germany in 2003. His compositions have been performed at international festivals including Donaueschingen Festival, ultrasound Festival (Berlin), Daegu International Musical Festival (Korea), Dialogues Festival (Salzburg), Klangspuren Schwaz. Lecture and concert tours have taken him to Mongolia (Roaring Hoofs Festival, Ulaanbaatar), to Kyrgyzstan (Silk Sound Road Festival, Bishkek), Vietnam and Indonesia (Cracking Bamboo, Hanoi / Bandung) and Ukraine (2 Days & 2 Nights, Odessa).
From 2005 to 2006 worked at the Institute of Musicology at the Eberhard Karls University in Tübingen and assumed the project management for "Jugend Komponiert" in 2007, a workshop for young composers organized by the Landesmusikrat Baden-Wuerttemberg. Since 2006 he has directed the Studio for Electronic Music (SEM) at the Mozarteum in Salzburg, where he was habilitated in composition in 2012. Teaching assignments lead him to the universities in Riga, Parma, Lisbon, Salamanca and Seoul. 2015 he was appointed professor and head of the Institute for New Music (INM).