To poach the chicken, place raw boneless, skinless chicken breasts in a large pot with salt and enough water or broth to cover it by at least one inch. Bring to a simmer over medium high heat, reduce the heat and simmer for 30 minutes, until the chicken is white throughout but still moist.
While the chicken is cooking, chop the onions. For the best texture, chop everything by hand rather in a food processor.
Remove the mint leaves from the stalks and chop them very finely along with the cilantro and radishes. Discard the stalks. The key is to make sure the herbs are completely dry before chopping.
Remove the seeds and pulp and then dice the tomatoes finely.
Wearing gloves, remove the seeds and interior from the jalapeño pepper and mince the pepper into tiny pieces.
Once the chicken has cooked remove it from the liquid (reserve broth for another purpose) and cool slightly. If you're using leftover chicken or rotisserie chicken remove any excess fat and skin. Shred it into thin strips using two forks or your fingers. Then dice it crosswise into small pieces.
Combine the chicken and chopped mint, cilantro, onion, tomato, radishes and jalapeno pepper in a large non-metallic bowl.
In a separate bowl, whisk together the lime juice from two limes, bitter orange juice, olive oil, plus salt and pepper.
Pour the lime juice mixture over the meat and vegetable mixture and toss lightly with a fork.
Chill in the refrigerator for 30 minutes or more to allow the flavours to merge.
Serve as a side salad or spread scoops of chicken salpicón on top of crispy tostadas and garnish. Options include slices of avocado, slivers of red onion, sprigs of mint and/or cilantro, crumbled cotija cheese, queso de Zacapa or crema Mexicana drizzled over top.