Spread tortilla chips evenly on a half sheet pan. Set aside.
Heat oil in a large nonstick skillet over medium. Add pork and shallot; cook 3 to 4 minutes, breaking pork into pieces with a wooden spoon. Add garlic, ginger, and fish sauce; cook 2 to 3 minutes, until pork is browned and garlic is aromatic. Use a slotted spoon to remove pork from pan and sprinkle evenly over chips. Spread kimchi evenly over pork.
Combine Greek yogurt, Sriracha, water, vinegar, sugar, salt, and pepper in a small bowl; mix well. Spoon yogurt mixture evenly over nachos. Top with green onion and watermelon radish.