battle for
To fight or compete to win or gain control of something. The soldiers have been battling for control of the border for days now. Paula and I are currently battling for a big promotion.
battle for something
1. Lit. to fight to gain something. The army battled for the town until they had defeated its defenders.
2. Fig. to attempt to win or gain something by struggling or arguing. Both of them battled for Kristina's attention.