Preheat the oven to 400 degrees F. Line two baking sheets with parchment paper.
Prepare the radishes by washing them and trimming their tops and bottoms. Run each radish through a mandoline to get thin slices. If you do not have a mandoline, use a very sharp knife to carefully slice the radishes.
Toss the radish slices in olive oil in a mixing bowl until they are very lightly coated. Transfer them to the baking sheets and spread them out without overlapping. Bake for 13-15 minutes or until they crisp up, shrink, and become wrinkly. Check their progress starting at 10 minutes to make sure they don't burn.
While the radishes are baking, prepare the other ingredients by dicing the bell pepper, serrano pepper, avocado, and cilantro. Drain and rinse the black beans. Shred the cheese if it's not already shredded.
When the radishes are ready, transfer them all to one baking sheet (keep the parchment paper underneath them). Push them towards the center without overlapping. Top the radish chips with the chopped bell and serrano peppers, black beans, and cheese.
Bake the nachos for an additional 3-4 minutes or until the cheese is melted. Take them out of the oven and top with avocado, cilantro, and a squeeze of lime juice. Divide into 2-3 servings and transfer to serving plates. Enjoy!