This solution was made when the online first released. I have tweaked the solution here and there from mentions in the comments. If their is anything that doesn't feel right in the solution then please feel free to correct me and I'll make adjustments.To get this achievement you must reach rank 22 on Red Dead Online which will unlock you the 'Small game arrow pamphlet’ This ammo crafting Pamphlet is the first one you can get to make progress towards this achievement.
Once you have reached said rank, you'll be able to purchase the pamphlet from any of the 5 Fence shops around the world for a price of $350 (14 gold bars)
Once purchased, you’ll need to open your satchel and manually read the pamphlet recipe which will teach you how to craft small game arrows. To craft small game arrows you will need to purchase 25 arrows (max is 10. So you'll possibly need multiple crafting sessions) from any gunsmith or general store around the online world.
Then you’ll need to kill and pluck birds to get flight feathers. You’ll need a total of 25 flight feathers. A great place where you can get a lot of birds at one time, mostly flying in packs is ‘Twin Stack Pass’ just below the ‘W’ in ‘New Hanover’.
When you have all the materials ready. Either find an open bit of land outside of any towns and hold ‘Y’ to rest. Then ‘X’ to craft. Or you can go back to your camp and craft the Small game arrows at the camps fire.
Find the small game arrows on the crafting menu under ammo and begin to craft your 25 Small game arrows until your achievement unlocks
Or if you don’t fancy going out your way to craft arrows, then you can always wait until you hit rank 28 which will then unlock for purchase the split point pamphlet, an ammo crafting pamphlet for $385 that only requires you to craft any type of ammo (rifle,repeater,pistol etc) at the camp fire.
Here is a clip of me purchasing the Pamphlet from the fence once reaching rank 28.
Here is a clip of me crafting the split point rounds. You can use this as an example on crafting the small game arrows. When I recorded this I’d gone for the spit point first as I wasn’t in any rush to bash this achievement out.
People have reported that you must craft all 25 in one online session as I’ve heard that your progress may be reset quitting out of the game or joining another session. Not sure if this is true but craft all in one session just in case.I will update the solution further once I have some more time on my hands. Thank you for your comments.