It depends. The Rambam defines a tzadik as someone whose zechusim are more than their aveiros. According to that definition, anyone can be a tzadik – we just don’t know how Hashem views each person and judges their actions, so we don’t know who is or isn’t a tzadik. We can make assumptions based on what we do see, but we may not be correct.
Chassidim usually use the definition given by the Baal HaTanya. Chassidim believe that a tzadik is someone who was selected for the role by Hashem. The role can’t be attained by a person, it needs to be a gift from Hashem. The tzadik has their human instincts for any inclinations completely subdued, and experiences pure d’veykus. The tzadik’s job is to act as a vehicle to raise up others, to help them get closer to Hashem.
According to the chassidic definition, almost nobody can become a tzadik – only a few people who Hashem picked. That doesn’t mean you can’t be a good, caring person, of course!