Heat about half an inch of oil in a heavy skillet or deep pot set over medium-high heat. When it’s hot, but not smoking (a scrap of bread or the edge of a tortilla should sizzle when dipped in), fry as many tortillas as you like until golden and crisp. Transfer to a plate lined with paper towel to absorb the excess oil, and season well with salt.
To make the ceviche, in a large bowl combine the fish, tomato, cilantro and chili. Add a generous amount of lime juice and season well with salt. Let the mixture sit – the lime juice will “cook” the fish – for 10 minutes. Taste and add more lime juice, if you like.
Serve the ceviche, using a slotted spoon to drain off excess liquid, on the crisp tostadas, topped with salsa verde, avocado, radishes, cilantro and lime wedges to squeeze over it all.