Such things should be based on the character actions in game, not on the time a player remained in Planeshift. Some people pass their whole lives without being famous, others are famous even as children.
Also there is nothing that really would fall on the category of "heroic quests" right now in PS, and once they are available, they should be not quests per se, but some unique types of GM Events that never happen twice. They should have several challenges ahead and dangers as well.
For me to become a famous hero your character should do something "heroic", like the examples below
1) Classic - Save many lives, a town, a region or the world from something provoked by an "evil". I.E.: Be the main responsible for leading/defending Yliakum first level against a mass invasion from the Stone Labyrinths, etc.
2) Populist(Grey area) - Improve the life conditions of the lower classes, and become some kind of "hero" in their view. I.E.: Making charismatic speeches and giving beggars and poor people aid to get a new life, etc.
To become an infamous and known villain your character should do a "great evil" like
1) Classic - Kill/Steal/Beat innocent people, destroy villages/cities/etc, take over a town and become its tyrant, etc.
2) Populist(Grey Area) - Exploit the ignorance of the lower classes for a selfish goal by promising them a better life among other rhetoric and demagogies, etc.
Although being a known villain means people would rally against your character thus it would not be an advisable path for a smart "evil" character.