[16][17][18] By winning the World Junior Chess Championship (U-20), held in the Brazilian municipality Matinhos 3–15 September 1994, Helgi automatically became a GM.
[20] Nevertheless, during this period he had some notable tournament's successes, for example he tied for first place in 1997 at the open international tournament Politiken Cup in Copenhagen[21][22] and in December that same year he competed in the FIDE World Chess Championship in Groningen where he knocked out Miguel Illescas[23] in the first round, then in round 2 he was eliminated from the competition after losing to Artur Yusupov.
[24] In 1999 Helgi showed solid and strong performances in many international tournaments[25][26][27][28][29] as well as sharing first place in the Icelandic Chess Championship with 9½ points out of 11.
[40][41] As a champion of the country in open section, Helgi accepted the opportunity to play for the Icelandic national team at the chess Olympiad, held in Batumi Georgia, 23 September – 6 October 2018.
[42] Helgi continued his chess activities after the Batumi Olympiad, for example he shared first place in the Pomar Memorial Open, held in Palma de Mallorca 26 November – 2 December 2018.
[45][46] At the European Individual Championship, held in Reykjavik 26 August – 5 September 2021, Helgi got 7 points out of 11 and ended in 35th place in a very strong field of players.