There is a group of 3 trees, near a wooden tower, west of Anarchy Acres (and north of a umbrella shaped excavation). See map below.
Search those trees for a Battlestar Item. The Battlestar Item is generally at the easternmost tree amongst those three trees.
Collect the Battlestar.
The location is west of Anarchy Acres, marked with the red circle. "X" marks the spot of the tree where you can find the Battlestar.
- 10 Battle Stars