Regardless of which version of Adam you defeat, you will get this achievement.
The first video is the fight with normal Adam. You will most likely get to fight him if you play normally without following specific instruction. Beat him and you’ll get the achievement. The video is not mine and credit goes to the creator – BrokenGamezHDR.
The second video is the fight with a supposedly a tougher version of Adam. You can only get to see him if you decide to banish (continue hitting and killing them after they lose) all the other bosses, except Channel. The video is not mine and credit goes to the creator – Pascal Desrochers