Really, all we need to do is support the brain to achieve immortality.
That's all the body is: Support system for the brain. Well, non-evolutionary speaking.
Step 1: Support the brain outside of the human body.
Step 2: Translate the brain to something indefinitely durable. I.E. won't succumb to Alzheimer, dementia, brain-damage, etc.
Whether that's brain-uploading (which has it's own philosophical issues) or replacing the neurons with a more durable analog, or basically bolting on new hard-drives to your brain that the brain can, over time, migrate into as new connections are formed and the various functions of the brain (memory, learning, sensation, thought, etc) are taken up by the silicon brain. Then even if you lose your original meat-brain, it'd be no more of an issue for you than if you were to lose a few dozen brain-cells right now. Relatively minor loss, getting even more minor as you bolt on more and more space and take it up. Basically the same as the second way, with some differences. (I.E. bolting on whole-cloth parts and waiting for it to be engaged versus replacing each connection individually, keeping the original connections versus making them irrelevant, retaining some semblence of the original neural structure versus "Eh, as long as it thinks, nevermind the structure" of bolt-on)
Bam, immortality. All you need now is some way to manipulate reality (hands, or radio-controlled nano-particles, or organic meat-sacks grown around a radio receiver instead of a brain, whatever) and to sense reality (cameras, aforementioned meat-sacks) and you're golden~