Collect 5 Coyote pelts.
This early mission is incredibly easy. Coyotes are very common in the wild and you shouldn’t have much trouble finding five to kill and skin.
Collect 5 Deer pelts.
Deer in Red Dead Redemption are not hard to find at all. Just riding between MacFarlane Ranch and Armadillo you’ll likely see more than five. Kill them and take their hides as your own.
Kill 5 Wolves with your knife and collect 5 Wolf pelts.
While these objectives aren’t overly difficult, the requisite of using your knife rather than a gun does make things more difficult. The wolves themselves shouldn’t be overly hard to find. They show up all over the place. That said, knifing them can be a pain. The key is to just be quick about it. Pick one and kill it before the rest of the pack can come to its rescue. Continue this until they’re all dead.
Collect 5 Boar tusk and 3 Armadillo carapaces, not counting those already in your possession.
This is probably the first mission that will give you much trouble. This is for a number of reasons. Killing armadillos? That’s easy. Killing boars? Not so much. While a good shot to the head will bring them down the same as it does anything else, boar are nonetheless fast and powerful. More often it will find you before you find it, and your first sign of its presence will be it plowing you over. If you let one knock you down it will come right back to hit you again.
The key here is to activate your dead aim the second you realise there’s a boar coming for you. Hopefully that should give you the time you need to get a shot off before its tusk is embedded in your rear. Beyond this, boars can just be hard to find. Even in their regular nesting grounds, it is more or less random as to whether you’ll spot one. It can take several days to find one, let alone enough for five tusks.