Heat 2 tablespoons of the butter and 2 tablespoons of the oil in a large nonstick skillet set over medium-high heat. Once the butter melts and bubbles, add the fish fillets in a single layer, without overcrowding the pan (you can also cook them in two batches).
Sear for 1 to 2 minutes per side. Before flipping, run a metal spatula under the fish to make sure there is a layer of butter and oil beneath the fish to make it easier to turn. Flip and cook for 1 or 2 minutes on the other side, until the fish is cooked though and can be flaked with a fork.
Place the cooked fish on a serving platter.
Add the remaining 1 tablespoon butter and 1 tablespoon oil to skillet, scrape the bottom of the pan well. Add the garlic and chiles guajillo, stir, and cook for half a minute before adding the slivered almonds. Stir as it all browns and crisps, no more than a minute. Scrape over the fish. Serve with halved limes and insist that your guests squeeze lime juice over the fish before they eat it.