As Reiman has pointed out, (b) is incorrect due to the tautology (i.e. using a word or phrase when a similar word or phrase has already been used). In fact, the use of however is also a tautology in (a). Also, the use of 'has' in this sentence does not make sense. It probably should be - 'Although she tried her best, she failed', because it is pretty clear that it is an event that has already been completed. If for any reason you wanted to use the present perfect tense (i.e. 'has') it should be in both clauses: 'She has failed, although she’s tried her best'; or, 'Although she’s tried her best, she's failed.' You might use this tense if the action has very recently been completed. The word 'however' could only be used implace of 'although' in sentence (a). I hope this isn't confusing!

Well (a) is more positive, since you are remarking the fact that she did her best. (b) is kind of more objective and negative, since you are emphasizing the fact that even when she tried her best, she lost! You have to notice that, you will have to chose to use in sentence (b) either the word "Although" OR "however" cuz, if you use both, it sounds over fabricated! OK i wish it helps!

Hi Yuko They are both OK, but they have slightly different emphasis, like this: a) she failed although she did try her best. b) despite the fact that she tried her best, she failed anyway. For both sentences you should use either 'although she tried her best...' or 'although she had tried her best...' In written English, you would not normally use "she's" when you want to say 'she has'.