Process first 10 ingredients in a blender or food processor until smooth, stopping to scrape down the sides. Cover and chill sauce for up to a week.
Bring 6 cups water to a boil; add shrimp and cook 2-3 minutes or just until shrimp turn pink. Drain and rinse with cold water. Chill up to 24 hours.
Peel shrimp, leaving tails on; devein, if desired.
Stir avocado into sauce; spoon sauce evenly into 6 chilled martini glasses or small bowls. Arrange 5 shrimp around the edge of each glass, with the fat part in the glass and the tails hanging down the sides of the glass; garnish, if desired, with lime slices. Serve with lime-flavored tortilla chips.