To obtain the For Our Princess side adventure in The Legend of Zelda: Tears of the Kingdom, speak with Penn at the Foothill Stable during the Potential Princess Sightings side adventure. For this quest, follow the road north of the stable to reach a cave with a skull above it.
Inside you’ll find two guys in their underwear. You’ll take their place to explore the cave with nothing but your underpants. Inside the cave be sure to collect the weapons scattered around (mainly on the right side) and fuse them with materials to make them stronger to fight the creatures inside. Please note that one of the monsters has armor.
Once you’ve defeated all the occupants of the Foothill Monster Den, exit the cave and speak with the two guys. Next, report back to Foothill Stable to complete the quest.