Most likely your first encounter with a Giganto Monster will be the Hermit Drill Crab, in the Weasand of Cados. Do not underestimate Giganto monsters. You may not even be able to attempt this guy just yet. However Lv 50~ should be fine. Nothing special, just kill one and you get the achievement.
If you don't end up getting this guy, just note his location for later as it will contribute to the overall progress of Big Game Hunter