Slice the yellow onion into thick rings and cut the chicken breast into thin strips.
In a medium bowl, whisk together the arrowroot powder, light beer, garlic powder, and smoked paprika until a smooth batter forms.
Dip each onion ring and chicken strip into the batter until they are fully and evenly coated.
Place the coated onion rings and chicken in an air fryer basket in a single layer, misting them lightly with olive oil.
Air fry at 375°F for 12 to 15 minutes, flipping halfway through, until the exterior is golden brown and crispy.
While the rings cook, stir together the Greek yogurt, lemon juice, sea salt, and black pepper in a small bowl to create the zesty dipping sauce.
Serve the hot onion rings and chicken strips immediately alongside the chilled dipping sauce.