The Dome Shard is a Shard obtained in Cerulean Cave or by mining Red+ mining spots in Mt. Moon or Turtle Cove. When defeating or catching Pokémon on F4 of Cerulean Cave, there is a rare chance of the Pokémon dropping a Dome Shard. Don't get too excited about getting a Dome Shard, since it will take you a long time to obtain 100 of them.
100 Dome Shards can be used to revive a Kabuto.