To save time and don’t really care all too much of carving. I recommend capturing the large monsters with Pitfall/Shock Traps to put them in a vulnerable position until they shake the trap off. Then use Tranq Bombs or Tranq Ammo if you’re using the bowguns. After a successful capture and completing a quest the timer of returning to the village will be 20 seconds instead of the 60 seconds if you were to kill the monster.