Anime: In the anime episode For Ho-Oh the Bells Toll!, he comes off as a proud and arrogant person with a slight superiority complex and exhibits a near-religious fervor for Suicune, challenging Ash for daring to say that he'd met the legendary beast. This may just be a form of jealousy on his part, for Ash had also seen Ho-Oh as well, while he has yet to encounter any himself. In the same episode, when he finally saw Suicune, he tried to capture it partially for ego gratification, ironically making him no better than the people who he's mentioned are unworthy for it. This is somewhat interesting compared to his appearance in The Legend of Thunder! when he mentions Suicune only once, and then only in reference to the other beasts.
In The Legend of Thunder!, he assists Jimmy, Marina, and Vincent in their battle against Attila and Hun. Marina falls for him because he wears a cape.
He is apparently very close friends with Morty, who is also an expert on the Ecruteak legends. Morty acts as Eusine's voice of reason, trying to convince him to calm down and ease up, but to no avail. When Eusine leaves suddenly at the end of the episode, Morty's lack of surprise indicates that this has happened before.
Manga: In Pokémon Adventures he is quite the showoff, especially towards women, performing flashy magic tricks and even giving out autographed pictures of himself. He flies around on a Jumpluff. He seems to be a close friend of Morty's, as the Gym Leader is helping him in the hunt for Suicune.
He is first seen being spoken of by Morty, who states that Eusine had him use his powers to try and find Suicune, to no avail. After Morty is defeated by Suicune he contacts Eusine, who goes off to catch it himself. During his hunt he runs into Crystal, who accidently shocks Arckee with his Electrode, proclaiming them rivals and disappears. He then visits and old couple and tricks them into giving him Moomoo Milk by "curing" their Miltank. However Crystal followed him and found out that Eusine really put a berry in its mouth and manipulated the nice couple, to which Eusine doesn't seem to care. They then encounter Suicune, which turns out to really just be a Ditto sent by Team Rocket to distract them. The two of them were able to let Suicune escape and Eusine defeated the Team Rocket Elite Trio.
[credit to bulbapedia]