Seeing as this is titled "Toughest enemy in the game" and for a very first encounter, I would say Lavos in the Ocean Palace the first time through. I mean come on, you can't even defeat it.... that is, if you count this as an enemy.
Actually, you can, but the result is pretty much the same as if you didn't take him out.
And for me, the most difficult enemy would have to be Son of Sun. When I first played Chrono Trigger in '95 with only the Nintendo strategy guide to pull me through, learning his pattern was almost an impossible feat. There were no GameFAQs or anything around back then, so it pretty much reduced the entire battle to a guessing game -- at least I had Lucca's TabanSuit to manage me through the first couple times until I could beat his arse consistently.