This is a tricky one. If there was one easy answer, then the world would be a much more peaceful place than it is today. However, there are some general trends your advisor can follow.
The first is to try to use logic to convince the Emperor. This will most likely not work, but it is by far the shortest and simplest approach. If it works, great!
The next approach is not really part of your scope, but outlasting the Emperor is always an option. If you can start a movement that is still going when he is on his deathbed, you can win. Of course, that is obviously not the kind of thing you are looking for.
The real solution is to start small. Really small. If you cannot convince the Emperor to change his ways, he has to convince himself to change his ways. He needs to "discover" what you already know. He needs an environment conducive to learning what you preach. Of course, you don't have the power to make this a reality on your own; you're just an advisor. That's why you start small. Start within your own power. Perhaps you have been gifted control of a village or two. Or perhaps you are the head of a guild to whom you can preach. Or perhaps you just have to start within yourself and be the change you seek for the world. It all depends on the situation -- adapt as needed. Whatever core you choose, you will use it to create environments that help the Emperor see what you want him to see.
Obviously what you are creating is at odds with a tyranical emperor, so it is more than likely that, if he sees it, he will try to destroy it. His actions towards it will typically be destructive or controlling in nature. However, he is not the only one acting in this area. You also have a say in what happens (just as there are two sides in every argument). You also can focus more on this core than the Emperor can, because he has an empire to run. This gives you the equivalent of mechanical advantage.
However, you cannot just put up walls, insulating you from these actions. The Emperor needs to "discover" what you are showing him, so he needs to actually be able to interact with what you have created, and he needs to believe its on his terms. If you put up walls, his efforts to tear them down will more than likely destroy what you protected within. This is far harder to accomplish than merely isolating yourself, and will take skill. Hopefully the advisor has this skill (note to OP: it is entirely reasonable that an individual advisor cannot accomplish this because they lack the skill. I assume here that your world can support writing in such a skillful advisor).
Now it would be rude for me to just say "go find an advisor character with this skill" without explaining what that skill looks like, but it would also be hubris for me to claim that I know the one way to make this happen. However, I can share some observations which suggest the kind of shape the advisors skill should take.
The message should be tiered. Don't rely on everyone fully understanding the purpose of your rebellion, because then that limits who you can involve. The softest tier should be something that requires little to no energy at all to maintain, and it should be infectious. Show off your skills at understanding how not to be a tyrant: find something subtle and small that everyone needs and give it to them. In exchange, you can rely on that something existing wherever you go.
The next layer may call for more energy, but should still be subtle. It should be difficult for the emperor to stop, even as a tyrant. Capoeira may be a good example to draw from. Technically it's just a dance, and its very dangerous to try to tell slaves not to dance, even if you're a tyrant. It quickly makes them unproductive. However, those who understand the dance also understand that it is a martial art, capable of resistance. This gives you power because people like beautiful dances. If you can teach them how to refine their dance skills, they give you an opportunity to teach them more.
Above that layer is where the nature of the resistance becomes apparent. This is where you start to have to move slower. You can throw out hundreds of small tidbits to help people with their lives as you travel. You can change the dance to suit the times. The resistence... it needs to be palpable, and it needs to have a focus. This doesn't have to be the true focus of your efforts, but it needs to be something people are willing to sacrifice for. Those in the resistance might suffer losses as you try to convince the Emperor, and they need to be ready to accept them.
Finally, you have your core, the people you trust. These are the people who actually understand what you are trying to do, and have bought in on it. These people guide the resistance, for a plan old resistance is not what you need. You need a resistance when gives the Emperor opportunities to discover what you are teaching, and that isn't so simple. Your core would be those who you trust to shape the resistance to give opportunity after opportunity to change the Emperor's mind.
These are also the people you trust to stay the hand of the resistance when they achieve too great of a victory. The impulse in such an event would be to jump in and claim the spoils of the victory, but to do so might harden the Emperor's heart. These core individuals are the ones you rely on to keep the resistance from actually cutting into the Emperor's rein, and to find ways to convert those victories into win-win situations where the Emperor felt he was helped by your cause.
Once the Emperor feels like the cause is helping him, you will quickly find there is less need for resistance, and he is more likely to listen to your new approach to governance.