That challenge won't hold up. There is ample precedent for mandatory vaccination (excepting medical exemptions)

The article goes into a good amount of detail and information from both sides without arguing/favouring one. It focuses on the legal side rather than the vaccines themselves, which is nice.

All that said, I can't see them winning this one. In the article they talk about the provision in the NDA (sec 126) which makes it an offense to refuse a vaccination:

Every person who, on receiving an order to submit to inoculation, re-inoculation, vaccination, re-vaccination, other immunization procedures, immunity tests, blood examination or treatment against any infectious disease, wilfully and without reasonable excuse disobeys that order is guilty of an offence and on conviction is liable to imprisonment for less than two years or to less punishment.

This pretty clearly defines that it is an offense, so unless the lawsuit is able to successfully argue that this section of the NDA is a violation, they're sunk. Additionally, the fact that the CAF was able and willing to accommodate those who were 'unable' to get the vaccine and chose only to attack those who were 'unwilling' to is another mark against the lawsuit.