You should be able to take on the lion-like things pretty soon, if not already. Try leveling by fighting them, and obviously aim for lower numbers of enemies where possible. Beyond that, continue with the story but I imagine things will remain around the same difficulty as they are. I would strongly suggest doing a few of those Cie'th Stone missions, the earlier ones - look for anything that has a low difficulty.

As you improve your stats from fighting these missions (and a few enemies here or there inbetween) then you should get to the point that you improve to the level you need to be to comfortably beat the enemies.

I remember when I first got there I went straight to a adamantoise and tried to take it on and died in one stomp and just laughed.