First I have to say: Before watching this anime you should have played the game. Without knowing the game you don't get most of the jokes in the anime.
Story: Well ... this anime is like a special for the game. There isn't actually that much of a story that is told. The whole anime seems to be a little homage to all those monsters and strange creatures in the game which isn't really a bad thing.
Art: The Chrono Trigger anime is now 12 years old so the quality of the animation is not really up to date. Nonetheless I rated the Art rather high because of the great character design of Akira Toriyama which I really like.
Sound: No real Opening song is the first sing I have to say. The BGM sounds a lot like the original BGM of the game. It is ok. but old fashioned midi sound.
Character: Even though the main characters don't really appear in the anime I rated the characters of this anime rather high because of the high recognition value of the characters if you have played the game. The characters are those lovely drawn monsters/creatures in the game and you can see the love of the designers for the game.
Enjoyment: I really really enjoyed this anime because of the earlier mentioned high recognition value of the characters and the setting itself. It is a fine hommage to the anime and I really laughed out loud because of Johnny and the berserking Gonzales robot. Also as I mentioned earlier you can see the love of the game in this anime for example in the drinking contest or the race which were minigames at the beginning of the game.
Overall: I highly recommend this anime if you liked the game. If you didn't play it you shouldn't watch the anime because you don't get the jokes. If you can lay your fingers on this rather old anime you should watch it. If not.... well it was a good anime but not the greatest anime ever produced.