"Fighting for your principles" means that you're trying to get them established in society and to get other people to agree that these principles are important. "Living up to your principles" means embodying them in your own personal life, especially when it might involve some personal cost or sacrifice.
For example, consider the principle that "everyone deserves a living wage." A politician might fight for that principle by advocating for minimum wage laws or for comprehensive public education and job training programs. If it was discovered that this same politician had a nanny for his children to whom he was paying almost no salary, then this politician will have failed to live up to that same principle.