All right, all right ... here's the answer:
init, also known as "process #1," is hand-built by the kernel and it is not allowed to die. This message means, most likely, that it never successfully started. ("attempted to kill" is entirely a misnomer.)
The reason will be found in messages which precede this one. Usually, "reinstall and try again."
The part "not syncing" means that the operating system was not in the middle of a disk-write (good!) when it died.