Mihalik began his junior career in the Presov organization at age 16 with the club's J-18 team scoring 13 points in 44 games in his first season in 2003-2004. He split the 2004-2005 season between the J-18, J-20 and 1.liga (Slovakian Second Tier) after dominating both junior leagues. In just six games with the J-18 team, Mihalik had 4 goals and 8 points and a +18 rating. J-20 proved little test for Mihalik as well as the defenseman potted 6 goals and 16 points in 23 games with a +17 rating. With the senior team, Mihalik had 3 goals, 4 points and was -5 in 32 games. Mihalik, who was a fixture on Slovakia's junior tournament teams, continued his meteoric rise in being named to the Slovkian national team for the U18 World Junior Championships where he played well with a respectable +2 rating in 6 games in the tournament. The Tampa Bay Lightning were impressed enough to select Mihalik in the 1st round of the 2005 Entry Draft. The Lightning's decision was aided by Brent Sutter and the Red Deer Rebels of the WHL's decision to draft Mihalik in the 1st round, 36th overall of the 2005 CHL Import Draft. Vladimir accepted the Rebels' overtures and moved to North America to begin the 2005-2006 junior season. In December he was named to Team Slovakia for the U20 World Junior Championships where he played well with 3 assists in 6 games. Prior to the season he attended his first Traverse City tournament and Lightning training camp. At Traverse City, the defenseman had just 1 assist in 4 games. Over the summer Mihalik was traded from Red Deer to WHL club Prince George. In 2006-2007, after scoring 1 assist for the Lightning prospect team at the Traverse City tournament, he showed great improvement with the Cougars scoring 7 goals and 26 points in 53 games with 91 penalty minutes. In the playoffs, Mihalik contributed 1 goal and 3 points in 15 games with 17 penalty minutes.
The Lightning signed Mihalik to a 3-year standard contract on April 6, 2007. The defenseman again participated at the Traverse City prospect tournament where he tied for third in the tournament for scoring among defensemen with 1 goal and 4 points. Despite his impressive offensive numbers, Mihalik was chastized for not showing up to camp in the proper shape and for suffering a groin injury during the tournament. As punishment, Mihalik lost an opportunity to participate in Lightning camp and was sent directly to Norfolk Admirals camp instead. The defenseman spent the entire 2007-2008 season with Norfolk, improving greatly over the course of the season and becoming one of Coach Steve Stirling's most trusted blueliners, earning around 20 minutes a night of ice time. Mihalik finished his rookie season of professional hockey with 1 goal and 16 points with 68 penalty minutes and a +9 rating in 68 games.