Here are some activities for increasing your core XP:
♡ Health
Fist fights Brawling with people and winning gives you health xp.
Rowing a boat
Hunting Hunting and killing animals will grant you health xp. Using a bow gives you even more.
Fishing Successfully catching fish grants you some health xp.

♡♡ Complete Challenges in these categories: Herbalist, Master Hunter, Weapons Expert = 25150 XP per challenge. A total of 1425 XP for all challenges in these 3 categories.

ϟ Stamina
Sprinting Simply tapping X to sprint steadily gives you stamina xp.
Swimming Find yourself in deep enough water and Arthur will start to swim. Swimming constantly drains your stamina bar, but it gives good stamina xp as you do it. Just watch you don't drown.

ϟϟ Complete Challenges in these categories: Explorer, Horseman, Survivalist = 25150 XP per challenge. A total of 1425 XP for all challenges in these 3 categories.

☠ Dead eye
Hunting Hunting, killing, and skinning animals grants you dead eye xp.
Shooting enemies Killing enemies with a gun grants you dead eye xp.
Cooking Cooking at camp gives you a small amount of dead eye xp.
Camp chores Marked by black dots on the minimap, camp chores are easy little activities that you can carry out for some extra dead eye xp.

☠☠ Complete Challenges in these categories: Bandit, Gambler, Sharpshooter = 25150 XP per challenge. A total of 1425 XP for all challenges in these 3 categories.

Doing all Challenges gives you 1425 XP per attribute, enough to reach Level 8. That’s where XP progression stops but you can actually bring them to level 10 via outfit sets. The way this works is that every challenge category unlocks a piece of a clothing set after challenge 1, 3, 7, 10. So completing all challenges in a category gets you a complete set consisting of 4 pieces. Equipping all 4 parts grants you +1 skill bar on the attribute (=level 9). Doing ALL 9 challenges (90 tasks) then unlocks another skill bar (=level 10).

So really, the most straightforward way is to just do challenges, this gets you to level 8 with XP, to level 9 with the outfit set, to level 10 for having done all challenges. We’ll go through all other ways to gain attribute XP below as well. More detail about what challenge counts towards what attribute is also in the overview below.


More details :
Talismans and Trinkets have nothing to do with Core levels. They just provide small buffs. Also Upgrades to the way Dead Eye Functions is not linked to how much of the core you have, the core simply allows you to sit in Dead Eye longer. Improved versions of Dead Eye are linked to playing the game and completing certain missions. There is no way around this, as a result it may be impossible to Max out or even Rank up your dead Eye core even if you have done Everything, if you are still in the early part of the game.
Just about anything you do can increase your core rings. Hunting and skinning animals gives you points toward dead eye and health. Running and swimming get you points toward stamina.
Don't skip chores , don't rush through the game, but know that dead eye improvement is linked to story progression.
even discovering new herbs will increase core ring level (i think dead eye)

DOCUMENTED BUGS mainly effecting reaching 2/2 of deadeye bonus

BUG Warning #1: When you buy your very final piece of reinforced equipment. DO NOT Save the game right away, instead wait for all the pieces you bought to be displayed on the left side of your screen.
BUG Warning #2: when you complete your final challenge wait to see The Legend of the East outfit unlock before saving the game.
BUG 3: while its not required, there is a bug that prevents dead eye from maxing. Visit your wardrobe , change your 2 displayed Tailismans now Equip the Legend of the East outfit.

These are all the bugs I'm aware of that can prevent a player from maxing out their cores.

Unlock Survivalist Before Downes Ranch
   • Video  

Horseman 9 as Arthur ( make sure you have around ten +2 Health Tonics and Health and Stamina Shots for your horse )
   • Horseman 9 as Arthur Van Horn to Blac...  

Herbalist 9 as Arthur thanks to Insane Troll
   • Arthur survives New Austin sniper for...  

Dead eye also increases when discovering and picking herbs. Don't forget to do chores around camp, sprint around on foot, and drink your Valerian Root, Ginseng Elixir and Aged Pirate Rum as part of the progression has to be earned by just playing the game.
Trinkets and Talismans have nothing to do with your Core Completion.