Beating the game with characters unlocks other characters, to obtain the minions you must beat the game in certain orders or beating the arena, here is a pic of how to unlock the characters:
Once you have unlocked a minion simply beat the boss antiquated with the minion, the easiest is beating the first arena (way left of the map) and the character you unlock beat the first boss, achievement unlocked.
Video was done by TheLuckynr7
Also you can load your characters from the 360 version by loading the game up on your 360, click player statistics on the main menu and hit RT this will que them on the One.
Once you have done the first step load the game up on the XBOX One and go to the 3rd button in the bottom right corner of your button selection on the menu, hit A, then X to download all your 360 save data.