Neon Genesis Evangelion: Shito Ikusei

This game has Tamagotchi-elements to it. You play as Ryoji Kaji. You have to take care of Adam, or "Shito" as it is named in the game, in an embryonic state. You'll be able to make it evolve through different options ("Energy"-to control its level of energy, "LCL"-to control the different parameters of the amniotic fluid, "AT Field"-to increase Shito's energy shield, "Item"-to give medicine to Shito). It will evolve into different forms depending of its stats. You can then make it battle the three Evangelions of Shinji, Rei and Asuka.

You can also explore different places from the Evangelion anime as Kaji himself, talk to different characters and acquire different items for Shito.

Once you finish the game, a special game mode will be available to make Shito battles at will.