From VG247: “As part of the Week 7 challenges, youll need to make your way around the various Expedition Outposts to get your Battle Stars.
Youre looking for a red Exploration Outpost that has an X-4 Stormwing close by. Head in the blue doors and see what loot you find inside. Theyre easy enough to find, just make sure you have a weapon equipped or Rift-to-Go handy as there will be a lot of opponents nearby.”
Source: N4G PC Fortnite: visit the Expedition Outposts