Beglin played schoolboy football in his native city with Bolton and Waterford Bohs before joining Shamrock Rovers in 1980. He went on to spend 3 years at Milltown, making 4 appearances in Europe and scoring one goal.
In 1982 Beglin was part of the League of Ireland XI that toured New Zealand where they played the New Zealand national football team.
Beglin was the last signing made by Liverpool manager Bob Paisley when he joined from Shamrock Rovers for GB£20,000 in May 1983. He was gradually brought into the first team over the next 18 months by Joe Fagan, before being given regular games in the left back slot by new player-manager Kenny Dalglish as a replacement for Alan Kennedy in the 1985–86 season. He made his debut in the left sided midfield position on 10 November 1984 in the 1–1 league draw with Southampton at Anfield. He scored his first goal for the club 5 months later on 10 April 1985 in the 4–0 European Cup Semi-final first leg victory over Greek side Panathinaikos at Anfield. Beglin's 85th-minute strike put the tie out of reach for the Greek club. Liverpool won the second leg 1–0 to set up a showdown in the final with Italian giants Juventus at the Heysel Stadium in Belgium however a retaining wall collapsed during a riot at the "neutral" end, and 39 Juventus supporters died, in what came to be known as the Heysel Stadium Disaster.
Liverpool won the League championship and FA Cup, pipping Merseyside rivals Everton to both, with Beglin picking up medals for each. He also began playing for the Republic of Ireland, picking up the first of 15 caps. Then it all went horribly wrong for Beglin, just seven months after lifting the league and cup double, his leg was badly broken following a mistimed tackle from Everton's Gary Stevens in the League Cup Fifth Round game in January 1987.
Former manager Bob Paisley said that it was one of the worst leg breaks he had ever seen, joking that he would break his own leg to prove a point to the FA. Furthermore, Liverpool defender Alan Hansen stated that the tackle was "a mile high and an hour late". Recovering from the break, Beglin sustained a knee cartilage injury playing for Liverpool's reserves in October 1988 which effectively finished his time at Anfield.
In June 1989, he joined Leeds United, where he helped the club to become Second Division champions and spent periods on loan with both Plymouth Argyle and Blackburn Rovers before a recurrence of his knee injury forced him into an early retirement in 1991, when still only 27.
He also began playing for the Republic of Ireland, picking up the first of 15 caps. Then it all went horribly wrong for Beglin, just seven months after lifting the league and cup double, his leg was badly broken following a mistimed tackle from Everton's Gary Stevens in the League Cup Fifth Round game in January 1987.
Beglin is now a co-commentator for BT Sport and NBCSN and former co-commentator on ITV. He commentated for RTÉ in the 2014 FIFA World Cup. In the past for RTÉ he has worked on coverage of Premier League, UEFA Champions League matches and Republic of Ireland internationals. Beglin has also been employed by Liverpool as a voice–over artist for the club's official DVD and video releases. He is also the co-commentator in the Pro Evolution Soccer video game series since Pro Evolution Soccer 2011, alongside Jon Champion and later Peter Drury.Shamrock Rovers
Leinster Senior Cup (1): 1982
Football League First Division (1): 1985–86
FA Cup (1): 1986
FA Charity Shield (1): 1986
Football League Second Division (1) 1989–90