Upon physical death, the AI 'Brain Aids' send the brain's contents, and thus the person's essence, through a quantum-entanglements field and upload them to computers in the Imperial cloning facilities, where the person in kept inside such a computer until a new body has been built. Since Terrans can only physically die if they're burned in- and outside, vaporized or deatomized, this process seems impossible. However, the transmission only takes a few picoseconds; much shorter than even deatomization.Therefore, as long as the cloning facility's computers are intact, the Terran race is truly immortal. However, if the cloning station is destroyed and they fail, for whatever reason, to send the information to another station, the people inside will die completely.
Even this method isn't perfect. Due to the suffered trauma (both mental and physical), combined with the effects of the ransportation of 'living' data, the mind becomes slightly corrupted, and this will worsen every time. It is possible to fully repair the person's mind, but this is an extensive, difficult procedure that takes several years to complete; and depending on the subject the psyche may never restore. Following enough gruesome deaths, the psyche will outright destroy the mind.
It is also possible cut of the transmission from body to computer if you have quantum manipulation scramblers or inhibitors. If the Brain Aids are taken out before the brain itself is damaged, you can kill Terrans without them being able to upload themselves into the cloning stations' computers. The Brain Aids are quickly repaired by the Nanobots so this is fairly difficult; and old style resurrection is still possible of the brain isn't too badly damaged.
There are other ways (excluding the ones from 5 reliable ways to kill...) to kill Terrans, but those are classified. You'd have to go to war to find out how.
Of course, the most effective way is blunt trauma. While Terrans feel very little pain, there is still the shock, and the mind can be shattered by enough stress. The best way to pull this off is to shoot anywhere but the face, preferrably the limbs. Energy based weapons aren't effective, so fire based- or large ballistic weapons are the way to go. Mutilation also causes a great deal of stress and shock, if done right. Simply cutting off limbs and breaking bones just won't do. Be creative!
Long story short: lots of bodily harm - psychological stress - mental damage - death.