Upon starting, immediately head towards the first marked outpost. You'll encounter numerous Bokoblins and a few Moblin captains. Use Link's spin attack (hold Y, then release) to clear groups efficiently. Capture the outpost by defeating all enemies within its boundaries. Once secured, proceed to the next marked outpost. You'll likely encounter a more formidable enemy, such as an Electric Moblin. Exploit their elemental weakness if possible (e.g., ice attacks if you had them, but for Link, focus on strong combos and dodging their electrical attacks).
Keep an eye on your special attack gauge. Unleash it when surrounded by a large group of enemies or against a tough captain to quickly deplete their health and weak-point gauge. Remember to pick up any dropped materials, as they will be useful for upgrading weapons and completing side quests later. Don't rush too far ahead; ensure your allies are keeping up and not getting overwhelmed.