A faster way to get this is to join SOS flare sessions.
Special Arena missions are by far the fastest way (select 'optional' for these when you search) but they won't count towards the 50 arena quests... That's done in the Gathering Hub.
If you change your mission preference to 'optional' or 'investigation' then also manage to capture the monster...
You'll be working towards a few achievements like...
Complete 100 quests via multiplayer.
Complete 50 optional OR investigation quests.
Complete 10 SOS flares.
Capture 50 monsters.
Hunt 100/500 large monsters.
To capture you need to use a shock/pitfall trap when a monster is low on health and then do a couple of tranq bombs. You can craft more traps and tranq bombs mid game if you bring the required materials along.
Note* you will probably fail the mission a couple of times, kinda depends on the difficulty and the players hunter experience/skill. 3 faints and the whole team is out!
You will also likely join some sessions and your team will kill/capture a monster before you even get there...
Happy hunting :)