Beethoven was one of the greatest artists who ever lived. Not easy to point to only one achievement from his life. Becoming deaf and still composing wonderful music sounds difficult enough! One could argue his music was the best, but how can we stay objective and impartial in the question of beauty…
Rather, one can turn to facts, like historical facts, that can be supported by evidence. If so, Beethoven’s greatest achievement was to make way and raise the instrumental music, and the musician with it, to the highest level of art.
Until that time music was considered inferior to other art forms, like poetry or painting. Musicians were often regarded as any other manual labor profession, like a carpenter or a cook. Music was primarily to serve text, like an opera or cantata.
The might and power of the orchestra grew up in the Mannheim Orchestra, both Haydn and Mozart moved the flag forward, but it was Beethoven, who composed music with such emotional charge and constructed them with such finesse and perfection, that was unprecedented before.
He demanded respect to both music and musician. After him, music and its place among the arts, changed forever. This was his greatest achievement.