Attilio Galassini was born on May 23, 1933 in Roma, Italy. He started his soccer career with the famous Lazio club in Rome.
After playing for FC Rieti he joined A.S. Roma in 1953. Attilio failed to get any appearances for the Lazio first team and left the club in 1955 to join Hellas Verona. In the 1956-57 season he was a member of the Hellas Verona team that won the Serie B championship. In the 1958-59 season he helped Ozo Mantova in winning the Serie C championship.
Attilio joined Toronto Italia before the start of the 1960 National Soccer League season. The outside right helped Italia win both the National Soccer League championship and the playoff championship.
After spending the winter of 1960-61 playing for New York Inter in the American Soccer League Attilio joined Toronto Roma. He scored 11 league goals as Roma won the 1961 National Soccer League championship.
In October 1961 Attilio joined the Philadelphia Ukrainian Nationals. In March 1962 he moved to his former club New York Inter. He played for Toronto Italia in the Eastern Canada Professional Soccer League in the 1962 season. In the 1962-63 season he played for Chieti in the Italian Serie C. Then followed a spell with his old club Rieti.
Attilio passed away in May 2002 in Margerha in Italy.