Every living being in the material world is forced to experience being born, to age, to get diseases and finally to die. Nobody in the material world can escape death, luckily we have the vedas, which come from the spiritual world that can teach us how to overcome death anyway.
First some of the basics how the material world came to be. Once some spiritual souls developed material wishes and wanting to become gods themselves, they were given the material world by god to fulfill their wishes or they fell into matter, depends how you want to express it. The spiritual world is eternal and perfect and nobody has to die, but the material world is bound by time and fading away constantly. So we know what caused the material world to be now and this is the materialistic mind-set of the souls, if we count one and one together now, we can easily see that we need to undo the root cause to undo all that results from there on and this is:
To become free from death, one has to become free from materialistic desires and develop the desire to only serve god again, this will undo all material problems including birth, aging, disease and death.
However this is a really hard and slow process most of the time, so it is usually not achieved in one lifetime and even if it is achieved, that person will still die a material death, but then will not be reincarnated, this is the regular way to become free from death. Materialistic people may think, this is all illusion and they think someone so powerfull to be free from death would use his powers to dominate everyone, but this is actually exactly the reason they are in the material world. Spiritual beings have no desires to rule over others and subdue them, this is the root cause of the material disease and all other material diseases are just a result from that, that is why those desires have to be given up, if one wants to be free from the material diseases. Defectiveness does not exist in the spiritual world, the spiritual souls are all perfect and in the material world all the souls are defective and therefore the whole material world is defective, which again brings forth all other defects like birth, aging, disease and death. The material world is a place where the souls can be defective and experience the consequences of their actions through karma.
To become perfect again the mind-set has to be changed from having materialistic (egoistic) wishes to having spiritual (altruistic) wishes, desires and wishes cannot be given up, that is why they have to be changed, so just giving up materialistic wishes is not enough, since such a state cannot be kept up very long, since the nature of the soul is to have wishes and desires and to experience bliss. Being materialistic is just the wrong way to experience bliss.
Once that stage of being free from material wishes and desires is achieved and they are transformed into spiritual wishes and desires, the cycle of reincarnation stops and on death the soul is lifted up into the spiritual world and is given a spiritual body. One can have achieved that stage but still have a material body that will age, get disease and die, but this is because the karma is still there and has to be extinguished, this is the normal way. Being immortal should not be confused with being immortal in the material world in a material body, this is not possible, it is only possible in the spiritual world in a spiritual body. Only in very rare cases where yogis have developed high skills, they are able to consciously leave their body and enter in a spiritual body or even transmute their actual body directly into a spiritual body, but these are more stories known from hearsay and I would not count on it, developing such skills requires very high efford and I do not know if this is even possible in the current age to achieve.