His target is definitely to make a big contribution to Real Madrid, one of which is by defending the La Liga and Champions League titles. Maybe the Champions League will be Mbappe's main target, because one of the things he wants is the Champions League title, which he never got while at Paris Saint Germain.
Real Madrid did not give up on getting Mbappe, after their failure in the previous few seasons because Mbappe preferred to stay at Paris Saint Germain, this season they really succeeded in getting the signature of this young player. This completes their squad, especially in the front line which we know they really need, because in the front line there are gaps that have not been completely filled.
Of course, Mbappe will want to become the champion of La Liga, this is what he came for, he got bored in Ligue 1 and while he is at the peak of his career, he will definitely want to win as many trophies as possible. But if he stays in Real long enough, then he will have many opportunities to win La Liga and I think the Champions League as well, and although the second is much more difficult to do, it seems that Real is the team that has the greatest chance of doing this, given their 15 wins in this tournament.