Akihiko is pretty tough to date actually, not quite as difficult as (SPOILER)Shinjiro and Ryoji but he's pretty tough since I don't think the dating option opens up until late in his social link and assuming you said the right things leading up to it.
Also I double checked and I think I misinformed you Fynn, you do get access to Monad in New Game + right off the bat. The difference now is that in the console versions, Monad unlocked automatically if you were on the path to the true ending on a first playthrough. Whereas P3P changed it so you had to beat the the Death Shadow first, which unlocked Elizabeth/Theodore's final request and Monad. So she can totally power through a second playthrough if she wanted.