some information has developed at gamefaqs--http://boards.gamefaqs.com/gfaqs/genmessage.php?board=929668&topic=33437516 (too bad the gamefaqs topic will die in like 2 months..)
Damage: this award goes to the character who did the most damage in one fight. The best way to deal damage in a single attack is to hit a large party of weak enemies with a high level magic spell. You can further boost magic with Shield Rune's Battlefield spell, certain food/items temporarily increase MAG, and the Alert status. Hitting enemies with an element they are weak against will boost it even more. (thanks to Nogoodnamesnow/gamefaqs for testing and info from Iczer 1/gamefaqs, with further updates from Sasarai10)
Healing: this is a cumulative count and likely only counts the in-battle heals. So heal away! (information from Amy Valentine/gamefaqs and Tluhdatsi/gamefaqs)
Kills: Cumulative statistic, obviously.
Quotes for characters who get all 3 achievements (discovered by Amy Valentine/gamefaqs)
apparently, if a character gets all 3 statues and you check each when that character in your party, they say something.
Eresh: Is this...Eresh? I see...so,this is how she appears in the eyes of the others. (Sasarai10)
Faylen: M-me? Who the heck built this thing? (Skrybe)
Georg "Well! Not too shabby, don't ya think?" (Nogoodnamesnow/gamefaqs)
Jeane "Tee hee hee... How delightful." (Fetus_of_God/gamefaqs)
Killey "This has nothing to do with the Sindar, so I don't care." (Nogoodnamesnow/gamefaqs)
Kyle "Aw, why put the statue here?! Put it where the ladies can see it!" (Nogoodnamesnow/gamefaqs)
Lorelai "You mean I'm stronger than all the guys here?!" (Nogoodnamesnow/gamefaqs)
Lyon "The Prince deserves a statue much more than me!" (Nogoodnamesnow/gamefaqs)
Miakis: "Ah hah hah...How embarrassing!" (Nogoodnamesnow/gamefaqs)
Nikea: "Sure, the statue's nice and all, but couldn't they have rewarded me in food instead?"(Amy Valentine/gamefaqs)
Richard "Woo Hoo! I'm sure Mueller's proud of me!"
Roy "Now hold up a sec... You mean to tell me I'M better than the Prince himself? Ha!" (Nogoodnamesnow/gamefaqs)
Viki "Oh, is that a statue of me? I think someone made me a statue before... Or wait.... Maybe not..." (Nogoodnamesnow/gamefaqs)
Zerase "Hmph... Why go to all that trouble?" (Nogoodnamesnow/gamefaqs)