Firstly, there is indirect damage. This includes the entry hazard;
- Stealth Rock
- Sandstorm
- Status conditions, such as poison, burn and confusion
- Items such as the Rocky helmet and
- Leech seed
In terms of abilities;
- Mold Breaker makes Shedinja’s ability useless
- Aftermath
- Rough Skin
- Liquid ooze
- And a few more
There are also some move that can damage it, being;
- Struggle
- Future sight
- Beat up
- Doom Desire
- And the recoil from Shedinja using struggle
In summary
There are still a lot of things that can beat Shedinja, mainly things like stealth rock and status conditions.
Hope I helped?