Is it okay not to put the article "an" before "unbeatable"?
In this case both are fine. By saying "an unstoppable spirit and an unbeatable energy", the sentence sounds a bit more formal. Repeating the article is not necessary but it does help to add emphasis. While not using the article here is fine, it is not a hard rule that you do not need to repeat an article. It is dependent on the sentence and the context. Ex: I need some who is an effective communicator, team player and leader to fulfill the role. (Repetition of the article is not necessary.) Ex: I need an apple, an orange and a kiwi for the fruit salad. (You need to use the article before each item).