A borescope down the intake port can be used to check the back face of the intake valves and maybe valve seats for any sandblasted. The same can be used to also check the injector tips for damage. By putting the borescope down the spark plug hole it can be used to check the cylinder bore for scratch marks. Many bore scopes can take pictures of the view on their screen.
A dry & wet compression test as Shane suggests would give an indication how bad the damage is and how much engine life has been consumed by sand.
Having the above done by another independent mechanic who likely has a borescope that can take pictures of the damage and who can write a report on the compression test is really the path you should take. You also need an accurate quote on the repair (engine rebuild?) costs and hire car costs during the repair period.
Then you’d have the information likely needed to better discuss your options with Fair trading and/or making a claim for the consequential damage caused by your mechanics negligence in not installing the air filter correctly.
As is, I’d not want someone so incompetent as to not be able to fit an air filter correctly doing an engine rebuild. So I’d look to your mechanic to pay for the engine rebuild at another place of your choosing and foot the hire car costs (he can claim the lot on his insurance).
Best to chat to Fair trading to better understand the process and risks.