We have all wanted to take a creature from mythology and warp it to our own needs. There have been good ideas and bad born from this, and so I suppose I should mention some of the considerations of making this work.
The first is finding the creature. You need something that fits your comic, and adds to it. The usual temptation is find something really unique and go from there, but that usually doesn't work as well as you would think. There will just be something wrong about your use of it that strikes readers as wrong, and so the creature somehow just work as well as it should. On the other hand, using a variant of an established creature will also usually fail if you try to make it unique; you are trying to cash in it on its brand, but wanting something unique, which is just really weird. Either create something unique, or strive to get the creature right; this is one of those areas where there simply is no real middle ground.
You then want to research the creature. You want as much information as possible on it, both to make sure that pre-existing fans of the creature will not be too mad at you and for the sake of the illustrator. You want something that the illustrator can sink his teeth into while at the same time making sure that you are doing right by the creature. Although I can understand that iconoclasts would prefer to just wing it, you'll find that nine times out of ten your research will give you some additional inspiration, usually some minor bit of trivia that is incredibly interesting, making it easier to get your mind around the creature, and making it really come to life.
You also need to get the iconography of the creature right. Just like in an ecosystem mythological creatures fit a niche, and by staying in their niche they can add a lot to your story. This applies from something as simple as werewolves and people's fear of change and predatory animals to school ghosts and kids' fears of the unknown. Obviously they can come out of that niche once in a while, but using a monster in a non-traditional way needs to be seriously debated, and should be avoided if it is just for the sake of being cutesy. If you need to, do not be afraid to come up with something new just to feel a niche in your story if it looks like a bad fit.
Lastly, just have fun with the critter. If it isn't something you can have fun with, then either create something new or go with something else. If you are having problems breathing life into something, then the problem is either that it doesn't fit with your plans, or it just isn't something you like. Keep in mind that it does not need to have a unique personality; sometimes a monster just doing what it does is more than enough. Sometimes you do not need a new character so much as you need a plot device, and plot devices just do.
Make sure your monster fits the strip, and you should do fine. Don't just pull a creature from the encyclopedia, but summon it from your imagination and it should work out fine.