Preheat your oven to 475°F (245°C) to ensure a perfectly crisp crust.
In a medium mixing bowl, combine the plain Greek yogurt, finely diced cucumber, chopped fresh dill, lemon juice, and minced garlic. Season with a pinch of salt and pepper. Stir until the mixture is smooth and well combined. Set aside to let the flavors meld.
On a lightly floured surface, roll out the pre-made pizza crust to your desired thickness, ensuring it's uniform. Carefully transfer the rolled-out crust to a parchment-lined baking sheet or a pizza stone.
Evenly distribute the shredded chicken breast across the surface of the pizza crust, covering it generously.
Using a spoon, dollop the tzatziki sauce over the chicken. Spread it gently, being careful to leave some chicken peeking through for added texture and flavor.
Sprinkle the shredded mozzarella cheese evenly over the tzatziki sauce. Then, add the thinly sliced red onion rings on top to give a sweet and tangy crunch.
Lightly brush the edges of the crust with olive oil, ensuring an even coating.
Place the pizza into the preheated oven and bake for approximately 12-15 minutes, or until the crust turns golden brown and the cheese is bubbling and slightly browned.
Once baked, carefully remove the pizza from the oven and let it cool for a few minutes. Slice into wedges and serve hot. For an extra touch, garnish with additional fresh dill on top before serving.