Are you sure it has to be a quest? I managed to get one while free hunting in the woods. Also, longsword is the weapon I use most; so hopefully hitting it's head wont be a problem. I didn't know you could break specific parts for specific drops; that's really cool! Is there any way to find out what other parts of monsters are breakable or is it just a case of finding out by trial and error?
Knirisk beat me to it mostly but yes, generally tails can be cut or broken, at least if they're fairly long (the only tails that can't be broken that I can think of are the raptor boss tails (Jaggi is the first of them), qurupeco, and.. that's about it really) heads can be broken, from there, it's kind've a hodgepodge but some common ones are some part of the wing, sometimes the entire wing, sometimes a specific little bit, and in general if a monster usually has a huge defining physical feature it can almost always be broken.
While I'm here I'll also go over regional damage, in great jaggi's case he takes the most damage when you hit him in the head (not all breakable parts are weakpoints, but heads usually are a pretty good bet, if not the best; again, not always, it'll typically be obvious if they aren't), and takes fairly good damage everywhere else. Later monsters will, for instance only take decent damage to the main trunk of the body or head, and the rest of the body will only take minor damage. Sometimes the best area to attack are the arms, etcetcetc. There's also different damage charts for cutting and impact damage but generally they're fairly similar.
If you just need to know right now what parts are breakable and their damage charts, feel free to check out the wiki, just typing in monster hunter wiki should get you it. Right now it's still updating for 3U, but most of the 3 stuff is still fairly accurate.