Double first's ultimate achievement (4)
I believe the answer is:
twin
'double' is the definition.
(twin can mean someone's double)
'first's ultimate achievement' is the wordplay.
'ultimate' indicates one should take the final letters.
'achievement' becomes 'win' (a win is a victory or achievement).
The final letter of 'first' is 't'.
't'+'win'='TWIN'
(Other definitions for twin that I've seen before include "(Town) paired with another" , "One born with another" , "Lookalike" , "Castor or Pollux?" , "One of two duplicates" .)