So I'm guessing Stat boosts from him dumping all his points in a previous chapter to Dex. Plus "balance" as magic hits the surface (skin, hide, fur, feathers) first but bullets dump energy into single spot but travel at a higher speed than arrows so bone breaking along with penetration.
So I'm thinking Arrows penetrate with low initial damage but do damage over time with bleeding.
Magic is surface level dmg with low penetration so it does DoT with burn, freeze, shock etc but can be countered or "toughed out"
Bullets will impact and depending on surface will either penetrate and do damage along the path of the bullet with hydrostatic shock or will get deflected after dumping energy into the target without penetration.
Then since this is a game world and there are two distinct critical hits "Insta Kill" and "Crit Kill" I'm going to guess that which kill is determined by hit boxes and DMG percentage. Something like if someone used a sword and hit your arm for 40% dmg your arm is sliced but moveable, 60% and your arm is broken and hanging by a thread and at 100+% it's gone in a spray of blood. HaHeHeylo is able to do +100% in vital areas to get insta kills. Like you can cast a 1 hit kill spell or rip a tree out of the ground one handed but good luck casting if your lungs are filling with blood or controlling anything below the neck if the central nervous system is missing a chunk the size of a musket ball. So in that example the lungs filling with blood would equal a critical kill and the central nervous system hit would equal a insta kill.
In the case of a eagle or a bird they tend to have a thick breast plate bone but if it's broken even by something small everything behind the impact hole is as good as pudding.
Could be wrong though.
Edit* now we're at the cooking portioned of the story will a Korean story go the Japanese route of superior rice folded a thousand times in soy sauce = greatest culinary discovery ever! or go a different route?