Cut onions to about a quarter-inch thick slices. Pull apart the rings and set small inner rings aside for another use. Put slices in a bowl and cover with beer (or soda water, if you prefer). Let soak while other ingredients are prepared.
In a shallow bowl, mix edamame crackers, shiitake mushrooms and the sesame seeds together. In another shallow bowl mix the tortilla chips and Tajin seasoning. These are your two types of breading. Fill a third shallow bowl with flour. Pour liquid from soaking onions into a bowl for dipping.
One at a time, dip onion ring into the liquid, then dip into flour bowl to cover with flour. Then dip quickly back in liquid and then into one of the breading bowls. Make sure the breading gets all over. Place on a cookie sheet. Repeat with each breading until they are all coated. Refrigerate for at least 30 min. to set.
Heat fryer or skillet with an inch of oil to 365º F. Fry onion rings, several at a time, until they are golden brown and place on layers of paper towels to drain. Salt as each batch comes out while they are fresh out of the oil.