You must try your best to satisfy the boss. For that you will need to do the following things:
1. First know thoroughly what the boss exactly wants from you. This will help you execute your plan. Also know the working style of your boss.
2. Once you have known the working style and wants of your boss, try to do everything as much perfect as you want. This will help you to get the initial satisfaction of your boss.
3. "To err is human" is a very famous proverb. So it is natural that you can make mistake despite your best efforts. And as your boss is a perfectionist, he will naturally rebuke you for that. But you mustn't be disappointed and try to work more hard to rectify that mistake.
4. If ever boss gives you extra work outside your fixed schedule, you must respond promptly. The main thing boss wants to see is your sincerity and integrity. In case of extra work, you can show this more effectively.
By doing all these things, you can do the best of works even under a perfectionist boss. You just need to relax and make sure that things are working out perfectly. Then you will see that everything will be fine for you.