Having a beard for a man (when it is possible) is wajib (obligatory) in Sunni Islam by consensus of almost all scholars and schools of thought. One of the many ahadith cited as evidence for this is the hadith from Abdullah b. Umar narrating from the Prophet (saws):
انْهَكُوا الشَّوَارِبَ، وَأَعْفُوا اللِّحَى
Trim the mustaches and leave the beard (to grow).
from Sahih al-Bukhari also in many other books
There is a difference of opinion within the Shafi'i school whether it's highly encouraged or obligatory.
For a Muslim, a hadith with a command from the Prophet (saws) is generally taken to describe an obligatory deed unless evidence suggests otherwise (from the principle "al-amru li al-wujoob").
Based on this hadith and many others like it, the scholars do say that it is a sin to shave the beard. As for whether or not you won't be a good Muslim without it, I don't see the connection. Being a good Muslim encompasses a number of things, from belief in the heart to kind actions to acts of worship. Not having a beard doesn't directly reflect on someone's character or the purity of their heart. But if not having a beard comes out of an arrogance or intentional disobedience of the Prophet (saws) then I guess that could have effects on others parts of one's Islam.