In 1921, he won in Vienna. In 1923, he tied for 4-5th in Frankfurt. The event was won by Ernst Grünfeld. In 1924, he tied for 2nd-3rd with Carls, behind Wagner, in Bremen. In 1924, he won a match against Heinrich Wagner in Hamburg. In 1924, he won ahead of Post and Gruber in Vienna. In 1925, he tied for 5-7th in Breslau. The event was won by Efim Bogoljubow. In 1925, he tied for 1st-2nd with Wolf in Vienna. In 1926, he tied for 4-5th in Vienna. The event was won by Rudolf Spielmann. In 1927, he tied for 1st with Friedrich Sämisch in Mittweida. In 1927, he tied for 1st with Hans Müller in Vienna. In 1928, he tied for 2nd-5th in Vienna. In July–August 1928, he took 8th in the Amateur World Championship in The Hague. The event was won by Max Euwe. In 1928, he took 7th in Vienna. In 1929, he tied for 5-7th in Karlovy Vary, and also inaugurated the Vera Menchik Club as the first member. The event was won by Aron Nimzowitsch. In 1930, he took 3rd in Ebensee. In July 1931, Becker played for Austria at fourth board in the 4th Chess Olympiad in Prague. He won individual gold medal there. In 1931, he won in Vienna. In 1932, he won in Vienna. In 1934, he tied for 1st with Erich Eliskases in Linz. In 1934, he tied for 7-9th in Bad Liebwerda. The event was won by Salo Flohr. In 1934, he won in Vienna. In 1935, he took 3rd, behind László Szabó and Ernő Gereben in Tatatovaros. In 1935, he tied for 3rd-5th in Vienna. In 1936, he took 11th in Zandvoort. In August 1936, he played for Austria at second board in unofficial Olympiad in Munich. Becker won individual bronze medal there. In 1937, he took 4th in Teplitz-Schönau. In 1937, he took 3rd in Vienna. The event was won by Paul Keres.
After the Anschluss in March 1938, he tied for 1st with Ludwig Rellstab in Berlin. In July–August 1938, he tied for 5-7th in Bad Oeynhausen. The event was won by Eliskases. In December 1938, he tied for 4-5th in Karlsruhe. In June 1939, he took 5th in Vienna. Albert Becker was a Captain of the German team in the 8th Chess Olympiad at Buenos Aires 1939. He played at fourth board, and won team gold medal. In September 1939, when World War II broke out, he along with all members of the German team and many other participants of this Olympiad had decided to stay permanently in Argentina. In 1944, Alberto Becker took 3rd, behind José María Cristiá and Pablo Michel, in Buenos Aires. Becker was awarded the International Master title in 1953.
