It sounds awful, but I'm trying to unlock Mock and I was wondering if anyone had a way to kill of a monster fast. I think if I keep stressing it out it'll just run away at some point so I'm not too sure how to go about it.

You can always feed the life-shortening items like:
Nageel
Kasseitan
Teromeann

Sueki Suezo always works with its one week lifespan.

I didn't know Sueki Suezo had such a short lifespan! I was in the process of killing a market Zuum and God, did I feel horrible after the thing died.

I just did non-stop errantry. Thanks for the suggestions because I'm probably going to need to kill another monster at some point.

I feel terrible. :(

A cheaper method, which only works if you're patient or lucky, is to get a market hare and enter the
New Year's cup (4th Jan). The first monster you fight is the A-level Kitty, who normally flames you
or does something else similar. It's very effective, although you do feel a tad sorry for the
Kittyfood's.

Sueki Suezo is the best way for a clean conscience too. It dies in a week no matter what you do, so you don't have to feel bad. Also, if you bring it up on a week with a tournement, you might be able to get a little bit of cash out of the deal.

I can't find ANY store around here with the original Monster Rancher. =( *sigh*

Which one of the buyable drugs (Larox, Kasseitan, etc) give your Monster the biggest Lifespan hit?

Paradoxine gives the biggest lifespan hit, its around 18-20 weeks i believe.

Nageel only costs 1000G yet it takes away 20 weeks
of lifespan.