It gets hurt by:
Sandstorm or Hail damage,
Damaging status (Burn, Poison, Bad Poison),
Stealth Rock, Spikes or Toxic Spikes upon switch-in,
Teravolt and Turboblaze,
Flame Burst in doubles (as secondary effects ignore it),
Anything to change or negate Shedinja's ability (Role Play, Entrainment, Simple Beam, Skill Swap, Worry Seed, Neutralizing Gas, Gastro Acid, Mummy),
Moves that ignore Abilities (Photon Geyser, Moongeist Beam, Sunsteel Strike, etc.)
Curse by a Ghost-type (or used by Shedinja),
Self-inflicted fainting (Explosion, Self-Destruct, Memento),
Any Rock-Type attack.
BTW there's 18 types not 16.
Hope I helped!