She was born in Perth.
Fiebig initially graduated as a cellist from the School of Music, University of Western Australia, before commencing vocal training, occasionally marrying the two on stage, with her cello accompanying her own singing.
She joined Opera Australia in 2005 as a principal soprano. Her roles for that company include Susanna in The Marriage of Figaro (televised and recorded), Galatea in Acis and Galatea, Musetta in La bohème, Zerlina in Don Giovanni, The Plaintiff in Trial by Jury, Clorinda in La Cenerentola, Belinda in Dido and Aeneas, Papagena in The Magic Flute, Rose in Lakmé, Servilia in La clemenza di Tito, Karolka in Jenůfa, Gianetta in The Gondoliers, Adele in Die Fledermaus, Aphrodite in The Love of the Nightingale, Lisa in La sonnambula. In 2006/07, she was Mabel in Opera Australia's production of The Pirates of Penzance, alongside Anthony Warlow (the Pirate King), David Hobson (Frederic).
In 2008 and 2009, she performed as Eliza Doolittle in a national tour of My Fair Lady opposite UK actor Richard E. Grant. Fiebig sang the role of Sicle in Pinchgut Opera's 2009 production of Francesco Cavalli's 1644 opera Ormindo. In 2010, Fiebig was nominated for the Helpmann Awards' Best Female Performer in a Supporting Role in an Opera for Bliss and La sonnambula; she won the award for her creation of the role of Lucy in Bliss. In 2011, she sang Yum-Yum in Opera Australia's production of The Mikado which was televised on ABC Television. In 2012, Fiebig added the role of Pamina in Julie Taymor's English-language production of The Magic Flute for Opera Australia to her repertoire. In 2013, she sang Oscar in Opera Australia's production of Un ballo in maschera directed by La Fura dels Baus.
- Plant, Simon (18 April 2011). "Bohemian Rhapsody". Herald Sun. Melbourne.
- Helpmann Awards Winners 2010
- The Mikado review, ABC Arts, 18 November 2011
- "Spain's avant‐garde of the performing arts, La Fura dels Baus, to direct A Masked Ball (Un ballo in maschera) by Giuseppe Verdi", Opera Australia press release
- "Review: Un Ballo In Maschera (La Fura dels Baus, Opera Australia)" by Clive Paget, Limelight, 17 January 2013
- "Taryn Fiebig and Jud Arthur performing in Opera Australia's Falstaff", Books and Arts, ABC Radio National, 2 December 2014
- "Simon Cowell wanted me to be the next Kylie Minogue but I turned him down, says Melissa George" by Jon Wilde, Mail Online (4 October 2009)