In short, you can only do this with kernel level code. Either you'll have to modify your kernel from source, or write an application which has so many security vulnerabilities that it would not run on a modern OS unless you intentionally crippled existing security features of the OS itself.
If this pursuit is academic, then the link below should provide more assistance. If you are attempting to do something malicious, note that this approach will fail.
Finally, you should be aware that there is no valid or legitimate use case for this kind of process, save for some sort of draconian DRM mechanism that cripples the OS somehow, or maybe intentionally hiding processes owned by a certain user/group that handle important device drivers that even the ROOT user shouldn't attempt to slay/terminate/kill. On seLinux, QNX, or something that would go into a mission critical system with administrative user access, it would likely be to prevent rookie/newbie admins from shooting themselves in the foot.
Credits:
https://unix.stackexchange.com/questions/17164/how-to-make-a-process-invisible-to-other-users