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Decide if action is required. Talk to colleagues. Keep a record. Consider your options.
The first thing to do is calmly and rationally think through the whole situation. Is your boss really favouring somebody unfairly? Is it proving detrimental to the morale and productivity of you and your colleagues? You have to be completely honest with yourself and be certain that it's not just because the favourite is the best at her job. It's not unusual to feel jealous of someone who is having more success, so be sure you are not projecting your concerns about your slow professional progress onto someone else. One good way to try to get some perspective on the issue is to talk it over with some colleagues to see if they share your perception of events. If you do this, it's very important that you tread carefully. Don't go throwing accusations around and don't try to convince other members of your team of your interpretation of the situation. Just ask for honest appraisals to better inform your judgement. It's important that you don't try and turn the rest of your team against the person you believe is being shown unfair favouritism. This will not endear you to anyone or help your case. Avoid turning it into a topic for office gossip or rumour and maintain your professionalism. To help you get a clear picture of what is going on, it's a good idea to keep a record of instances where you think you have been treated unfairly, or there has been unwarranted favouritism shown. This could include examples of the other person consistently receiving more interesting and engaging jobs to do, or a significant imbalance in the rewards for similar work. You may need this evidence later, but first of all think of it as a way to carefully analyse the situation and gain objective information. You need to be exceptionally honest and rigorous when you record such incidents. Once you have fully taken stock of the situation you should think carefully about what options are available to you, and what the likely consequences of any action would be. You should try to clearly envision what outcome you wish to achieve before you go any further. Keep in mind that it's important not to allow a toxic situation to fester.