He has several titles on his showcase, twice winning the Brazilian Chess Championship (2005 and 2017), is a two time champion of the Sants Open in Spain (2009 and 2014), has five gold medals from the Pan-American Youth Chess Festival (in the sub 10 category in 1996 and 1997, under 12 in 2000, under 14 in 2002 and under 18 in 2005). He also won the South American Junior Championship three times (2006, 2008 and 2009) and in 2006 he won the 65th anniversary tournament of the Paulista Federation and grabbed the Latin American Cup in 2011.
Fier competed in the World Chess Cup in 2009, 2011, 2013, 2015 and 2017 and in the Chess Olympiad, the World Team Chess Championship, the Pan American Chess Championship for Teams and the Mercosur Chess Olympiad, winning gold medals in Mercosur and the Pan American Championship.
Currently, Fier lives in the European country of Georgia and is married to fellow chess player Nino Maisuradze, a native of that country and with whom he has a son.