Place the eggs in a large pot and cover them with water. Bring the water to a boil over medium-high heat, then reduce to a simmer and cook for 10 minutes.
Drain the eggs and transfer them to a bowl of ice water. Let them cool for 5 minutes before peeling.
Slice each egg in half lengthwise and scoop the yolks into a mixing bowl. Mash the yolks with a fork until smooth.
Add the mayonnaise, Dijon mustard, salt, black pepper, and paprika to the yolks. Stir until the mixture is creamy and well combined.
Spoon or pipe the filling back into the egg white halves.
Cut 6 olives in half lengthwise to form the spider bodies. Slice the remaining 12 olives into thin strips to create the legs. Place one olive half on each filled egg and arrange 8 strips around it to look like legs.