Place the eggs in a large pot with enough water to cover them by 2 inches and bring to a boil. Immediately remove from the heat, cover and allow to stand for 13 minutes. Drain and rinse under cold water to stop the cooking.
Meanwhile, place the avocado in a bowl and mash with a fork until fairly smooth. Add the mayonnaise, mustard, salt, and pickles and stir to combine.
Peel the eggs and sliced lengthwise in half; remove the yolks and place them in the bowl with the avocado mixture; mash until fairly smooth.
Place the whites, cut side up, on a platter. Fill a plastic bag with the avocado mixture and snip one small corner off. Push the filling towards the corner and pipe the mixture into the egg whites.
Quarter 6 of the olives lengthwise for the spider bodies; place on top of the avocado mixture. Cut about half the remaining olives in half lengthwise, and cut those halves across in very thin slices for the legs. Place 4 on each side of the spider bodies. Repeat until all spiders have their 8 legs.
Place the tomato paste in a small plastic bag and make a tiny snip in one corner. Pipe red eyes on the spiders. Alternatively, use a toothpick to drop the tiny red eyes on the olives.
Nutrition per each egg half: 59 calories, 3 g protein, 2 g carbohydrates, 4 g fat, 1 g saturated fat, 122 mg sodium