Place the eggs in a pot and cover with cold water. Bring to a boil, then reduce heat and simmer for 10 minutes.
Drain the eggs and transfer them to a bowl of ice water. Let them cool for 5 minutes, then peel off the shells.
Slice each egg in half lengthwise. Scoop the yolks into a mixing bowl and set the whites aside on a plate.
Mash the yolks with a fork. Stir in the mayonnaise, Dijon mustard, salt, and black pepper until the mixture is smooth.
Spoon or pipe the yolk mixture back into the egg white halves.
Cut 4 olives in half lengthwise to form spider bodies. Slice the remaining 4 olives into thin strips to create legs. Place one olive half in the center of each filled egg and arrange 4 to 6 strips around it as legs.
Sprinkle the eggs lightly with paprika before serving.