After completing the Objective, return back to Hieronymus to complete the mission.
When you have assisted the troops enough, a message in your log window will inform you of the completion of your Objective, with the experience points gained. Allied Notes will be granted after reporting back to Hieronymus.
After you zone into an area under Bastokan control and receive your tags, you can speak with the NPC you got your tags from and immediately complete this mission without having to attack anything. You of course, need to return to Hieronymus to officially complete it.
It's possible to do battles in areas under Windurstian and San d'Orian control after accepting this mission before heading to a Bastokan area to finish this mission.
Beastman Confederate forces are now planning full-scale sieges on republican strongholds within Bastokan territory. Join the struggle in these decisive Campaign battles and assist our troops of the 7th Cohors in defending these key strategic points.