After two years of training, you've learned the truth. Alhammarret has been using you as a go-between, selling intel to both sides and wiping your memories regularly. He's even concealed your nature as a Planeswalker. When you confront him, the sphinx unleashes a devastating psychic attack.
Alhammarret is too tough to defeat in physical combat. Exhaust his mental resources by making him draw from an empty library, and you win no matter what his life total is.
Alhammarret begins the game with 40 life.
As the game informs you, the duel is intended to be won by milling Alhammarret's entire library. Jace has some new tools for that in this duel, with two Jace's Mindseekers and one Traumatize, in addition to the three copies of Sphinx's Tutelage and one Psychic Spiral.
Alhammarret starts with 40 life and has many defensive creatures and ten pieces of countermagic. His plan is also to mill Jace's library, which you can use to your advantage if you draw the Psychic Spiral with a stocked graveyard. Note that Alhammarret doesn't have a Psychic Spiral of his own, so he can't turn your strategy against you the same way. The simplest way to win the game is therefore to resolve a Psychic Spiral while there are at least as many cards in your graveyard as cards in Alhammarret's library. Alhammarret's only answer to Psychic Spiral is Clash of Wills, so play around it, either by baiting them out before playing Psychic Spiral or simply by having enough extra mana to pay for it (that is, four more untapped lands than Alhammarret, since you need five to pay for Psychic Spiral and one fewer than the number of lands Alhammarret can tap for Clash of Wills).
One particular tip is that you can use Riddlekeeper's triggered ability to your advantage if you have Psychic Spiral and are confident you can resolve it. By attacking with all your creatures, you can mill yourself two cards for each creature you attack with, which may make your graveyard large enough to mill Alhammarret out with your Psychic Spiral.
Unlike the last encounter with Alhammarret, this time his defensive creatures are actually effective against Jace's creatures. The three Fog Banks and three Hover Barriers each blank the offensive capability of any one of Jace's creatures, in particular any of Jace's 5/5 flyers. He still doesn't have a way to permanently deal with a resolved Phantom Warrior, but it takes twenty attacks with Phantom Warrior to deal 40 damage to him, so if he gets out Riddlekeeper you won't be able to win that way anyway (even if you Psychic Spiral to refill your library, that empties Alhammarret's).