To all the people having trouble, try turning on auto-blocking in the options and don't run when enemies are near. Your character will automatically block anything that's blockable as long as you're walking normally / standing still.
After I found that out most encounters became a lot more manageable. Just approach them slowly, block their first attack and then counterattack with a combo you're comfortable with.
I do agree that the whole "tapping multiple keys at the same time and with precise timing" thing makes pulling off a good combo quite a bit harder than need be though. Means you've got to be real patient with your inputs, which can be tough when there's tons of stuff going on in a fight.
Also, if you're outnumbered while playing as a caster, try using debuff spells like Sana's sleeping gas. That way you can easily pick them off one by one. You can even re-apply the spell while they're still knocked out to keep them out of the fight forever. (well, until your MP runs out that is...)