There are a few levels of immortality.

 

Level 0 - Social Immortality

The meme that lives on forever, history books and your impacts on society through chaos. You die, but a part of you lives on.

 

Level 1 - Anthropocentric Immortality

You as yourself, live 'forever'.

This is also the most realistic and achievable level. In fact I would not be surprised to find we can do this today with current technology. CRISPR has allowed us to perform DNA splicing with so much ease anyone can do eugenics in their garage. In the last decade Google finished sequencing the genome. We know the primary cause of aging is telomere degradation which is cause by oxidation of your body. Increasing resistance to oxidation and regenerating telomeres is already a realistic thing that we as humans can do. We have already extended lives this way...

This level I do not consider 'true' immortality because you can still be killed by physical effects or bad upkeep managing your age and eventually you will succumb to entropy.

 

Level 2 - The Quixotic Existence

I think there's merit to this as I understand m-theory and quantum immortality is a valid postulation. That you are constantly on the edges of the worst possible fates only to be constantly cut off and 'you' redirect yourself. You here reading this will never experience those ends just like the ends you've dodged before. You constantly shy away from the end of probability until it reaches its limit. You live as a human for as long as possible along this curve of space until all probability reaches 0 and you finally blink out in the last possible universe of your conscious causal existence.

 

Level 3 - Absolute immortality

Achieving true immortality requires rejoining the universe, god, nirvana, whatever you want to . Somehow transforming your consciousness back into a higher level abstraction. You aren't as you are now, experiencing human understanding, but something more. As I would say, becoming one with the algorithm of reality.