Season the chicken with salt and pepper. In a medium dutch oven, heat the oil over medium high heat until shimmering and hot. Add the chicken in one layer and brown until golden on both sides. Transfer to a plate and set aside.
Add the onion to the dutch oven and cook, stirring occasionally until golden, about 9-10 minutes. Add the tomato paste and cook for 2 minutes. Add the ketchup, tomato sauce, 1/4 cup water, vinegar, brown sugar, chipotles, mustard powder and season with salt and pepper. Bring to a boil, reduce to a simmer, and cook uncovered until thick about 5 minutes.
Return the chicken to the pan and cover and simmer for 1 hour until the chicken falls apart. Remove from the heat and cool. Shred the chicken with 2 forks.
Preheat the oven to 375°F.
Arrange the chips on a large rimmed baking sheet in a single layer. Top with the pulled chicken and then the pepper Jack cheese. Bake until the cheese is bubbling and the edges of the chips are crisp, 20 to 25 minutes.
In a large bowl, gently toss together the avocados, onion, tomato, cilantro, lime zest, lime juice, and salt and pepper to taste.
Remove the nachos from the oven and top with the salsa, sour cream, jalapeños, and cilantro.