Island battle from two months back (4)
I believe the answer is:
guam
'island battle' is the definition.
(Battle of Guam, 1944)
'two months back' is the wordplay.
'two months' can mean two replacements for 'month'.
'month' becomes 'M' (standard abbreviation).
'month' becomes 'Aug' (abbreviation for August).
'back' says the letters should be written backwards.
'm'+'aug'='maug'
'maug' backwards is 'GUAM'.
'from' is the link.
(Other definitions for guam that I've seen before include "place in the Marianas" , "NW Pacific island with large US base" , "Largest of the Mariana Islands" , "North Pacific island, base for the US navy and air force" , "US island east of the Philippines" .)