They fought a fair battle with the enemy.
I have a question about style:
In German it would be considered very bad style to use e.g. a verb and an object from the same word root in one sentence (variatio delectat 
).
I think the same is true in English (“I fought a fight?”)
How do Italians feel abou that?
I’m really not sure here. I’ve used “He fought a good fight” before, I seem to recall this style being used in poetry, hymns etc. The Italian seems to work, I think.
Ah yes, I remember that one -
Hymn Lyrics - Fight the good fight with all thy might
We’d also often tell someone to “sing us a song” as in one of my favourites, Billy Joel with “sing us a song you’re the piano man” -
Billy Joel – Piano Man Lyrics | Genius Lyrics
I think these are probably exceptions though, as I can’t think of many other examples that don’t sound strange.
Anyway, enough about English in this Italian sentences discussions category 
Grazie per questi esempi Zzcguns. A dopo … (as they say;-)