the rules

First, we need to define "eternal life".

Eternal life is when you live forever, but there are exceptions. If the Earth explodes because of a supernova, or the universe dies of heat death, we will die too. Because first of all, it would be impossible to develop technology that could make us survive that, and second of all, we would just float trough space being extremely depressed and unhappy.

Things we would be able to survive are things like aging, hunger, murder, poison, extreme temperatues etc. What we could do to survive that, are things like turning ourselves into cyborgs or put our brains on microchips. But that would also mean we couldn't process flavours and things like that.

Operation phoenix

We could also do an operation phoenix (Rick and Morty) type of thing, where we put clones of ourselves in tubes of liquid, and the clones will wake up and get your consciousness when the real you dies. But the problem with that is that a murderer could also kill your clones so you can't come back alive again. Also, you would need to create a lot of clones wich would cost a lot of money.

So yes, it's technically possible to acieve eternal life, but it has its flaws.