Unicornucopia - UPDATE
Sorry for the delay on this, but I've just confirmed that you have to show the UNICORN a total of 11 times to the 10 characters, giving you the prerequisite 10 comments. LINCOLN counts as a comment, but SUPERBALL counts as a show but not a comment. This is probably what TellTale meant when they said that this achievement was "harder than you think".
The characters & situations are confirmed as;
MAX THE RABBIT-LIKE ENTITY
HARRY THE MOLEMAN
AGENT SUPERBALL (before cooking the UNICORN in the MICROWAVE)
JIMMY TWO-TEETH (while on the BENT METER)
HUGH BLISS (in the CRYSTAL)
HUGH BLISS (in the final scene)
(thanks to one of my alternate accounts for the confirmation!)
-=#=- Speed-Run Achievement Walkthroughs -=#=-.