For the tostadas: Preheat the vegetable oil in a deep-fryer to 350 degrees F. Line a plate with paper towels.
Fry the tortillas flat until completely crisp, about 1 minute. Drain on the paper towels.
Cut the tuna into 1/4-inch cubes, discarding large pieces of sinew, and place in a small bowl. Dress the tuna with 2 tablespoons olive oil and some salt and pepper and mix well. Add the shallot. Drain the juice from the lime supremes and add to the radishes in a small bowl. Add the supremes to the tuna mixture and mix well. Chop half the cilantro and add to tuna mixture. Add the remaining tablespoon olive oil to the radishes and season with salt and pepper.
For the chipotle aioli: Place the chipotles, mayo and lime juice in a mortar and pestle and blend until smooth. Slowly add the oil and season with salt. Spoon into a bowl.
To compose, spread about 1 1/2 tablespoons chipotle aioli on each of the tostada rounds. Place the tuna mixture on top of the chipotle aioli. Top the tuna with the radish mixture and the remaining cilantro leaves.
To cut supremes from citrus, first cut the peel and pith away with a knife, revealing inner segments, then cut the segments free from the membranes.