She was born in Dublin, Ireland to Raphael Walsh, a furniture designer and manufacturer from Navan, County Meath. In 1975, when Walsh was 16, she began studies at the Dún Laoghaire Institute of Art, Design and Technology in Dublin. She then continued her education at The National Film School in Beaconsfield, England, where one of her main influences was Bill Douglas, a Scottish filmmaker who tutored at the school. She later settled in London.

In 1985, Walsh wrote and directed her first short film, which was titled Hostage. She followed this up with her feature film directorial debut, Joyriders (1989), before transitioning into television work throughout the 1990s. Her television work in this period includes episodes of The Bill (1991–1994), Doctor Finlay (1993), Roughnecks (1995), and Trial & Retribution (1997–2002). In 2003, Walsh wrote and directed her second feature film, Song for a Raggy Boy, which won multiple awards at international film festivals, including the Best Film award at the Copenhagen International Film Festival. Her third feature film, The Daisy Chain, a horror-thriller film, was released in 2008.

Throughout the 2000s and early 2010s, Walsh also continued to work in television, directing series and television films, such as the BAFTA TV Award-nominated Fingersmith (2005), the BBC One film Sinners (2007), The Fifth Woman—a feature-length episode of the BBC series Wallander starring Kenneth Branagh (2010)—and Room at the Top (2012), the latter of which earned her a BAFTA TV Award in 2013 for Best Mini-Series.

In 2014, she directed A Poet in New York, which explores how Welsh poet Dylan Thomas died in New York at the age of 39. The film was made to mark the centenary of Thomas’ birth on 27 October 1914.

For her work on Maudie, Walsh won a Canadian Screen Award for Best Director; the film won a total of seven awards at the 6th annual ceremony in 2018. Walsh also won the award for Best Director at the 15th annual Irish Film and Television Awards in 2018 for her direction of Maudie.