Maybe others can find sources, but...
Who is a tzaddik (in the context of this question) is a large debate. Various groups believe different things. For example, in the Tanya, a tzadik is anyone who never has a sinful thought and never does a sinful did. A beinoni is a person who never does a sinful deed but does have sinful thoughts, and a rasha is anyone who has ever done a sinful deed.
According to the Rambam, a tzadik is a person who has a near perfect conception of Gd.
According to some views of the Gemorah, a Tzadik is anyone who does perfect teshuvah.
Now, how these things relate to olam habah also varies.
The Gemorah relates that Olam Habah is like a yeshiva class room. Those who are greater sit in the front row, and those who are not as great sit in the back row. How many rows close to the front counts as a tzadik to eat the Leviathon, is not so clear.
According to the Tanya, (I believe) each sin a person does creates a black thread in their clothing, and a black brick in their store hourse. Each mitzvah, creates a white thread and a white brick. So the Tzadikim would be all of those who have only white clothes and white store houses. (The store houses contain the rewards for their mitzvot, while the clothes provide social reward)
Now, according to the Rambam, none of the above applies.
According to all opinions, I believe, you have at least 2 classes of people in Olam haba, those who are great and those who are less great. (Based on the vision of a Tanna that went to Heaven and saw that olam habah was all mixed up. Those who were well respected in this world were nothing in the world to come, and those who were ignored in this world were giants in the world to come.) It seems, also that there might be 'beinoni' castes within Olam habah based on this view.
Lastly, also according to all opinions you have 4 classes of people. 1. Those who never make it to Olam Habah. 2. Those who make it to olam habah as part of the Jewish people. 3. Those who make it to Olam habah based on their merits. 4. Those who would not make it to olam habah on their own, but do make it to olam habah based on the merits of their descendants.
Those who eat of the leviathan, would be the greatest of those who make it to Olam habah. Though some also say (don't remember who) that everyone who makes it to Olam habah gets to partake of the feast in the days of Moshiach and techayet matim.