Question: What is the degree one should achieve, so he will not have to reincarnate?

It is written in the book Sha'ar HaGilgulim (Gate to Reincarnations, p.10) that "All the children of Israel must reincarnate until they are complete with all the NRNHY. However, most people do not have NRNHY, only Nefesh. This means that each person must correct only the root of one's own soul.

All the souls come from the soul of Adam ha Rishon, since after the sin of the Tree of Knowledge, Adam's soul broke into 600,000 souls. From the Light that Adam ha Rishon had, which is called, "Zihara Ilaa" (Upper Light) in the Garden of Eden, it dispersed into many pieces.

After the sin, good mixed with the bad and a great structure of Klipot was established, with the power to cling to Kedusha (Holiness). In order to beware of them, the Light was divided into small pieces, which are too small for the Klipot to suck from.

An Allegory: A king wished to deliver a great sum of money to his son who lived across the sea. Since all the people in the king's country were conniving thieves, he divided the money into pennies and sent them with a great number of emissaries, so that the pleasure of theft was not worth dishonoring the kingship.

In this manner, over time and in many souls, through illumination of the days, it was possible to sort out all the holy sparks that were robbed by the Klipot, by the sin of the Tree of Knowledge.

"Many souls" - that is the division into Inner Lights. Many days - that is a division into many outer Lights. And the bits accumulate into the great amount of Light that Adam ha Rishon sinned in. Then it will be the end of correction.

Thus, everyone is born with a small piece of the soul of Adam ha Rishon and can only correct that which belongs to one's own share. When he corrects that piece, he no longer needs to reincarnate. 

However, each individual has the labor of choosing to be righteous, correcting what he must, through his efforts in Torah and Mitzvot, according to the root of his soul, and then he is complete.