Juice 1 lime into a cocktail strainer. Run the pulpy part of the lime around the edge of the lowball glass to get it wet, then invert the glass and roll the edge in the tajin.
Add 1 oz of tequila and the peach slice to the bottom of your lowball glass. Muddle well until there are no large chunks of peach remaining, about 2-5 minutes depending on the juiciness of your peach.
Add the remaining ingredients to your cocktail shaker and add ice. Shake well.
Pour the cocktail through your strainer into the peach mixture. Stir well with a long-handled spoon and top with ice.