It's important to realize that each attempt at the Animated Horn is like an attempt on the Dynamis Lord - you're only going to get one shot at it during your run; and it's going to be one or the other, never both.
The Animated Horn spawns at I-7, in a nook on the east side of the cliff. It will appear only after defeating the 15 demon generals and releasing the spirits from the prison of souls. You can backtrack to the northmost general tower, and head eastward past where the time statue was, hugging the south wall until you get to I-7. There are some eyes and a statue to the southeast, and an eye north of the Animated Horn's location, but in between these two is an ideal camp for fighting the Animated Horn, if you can get all members to it aggro-free. Another camp is southeast of the Horn's location, it is a safer camp but a longer pull, and every second counts in this fight.
Befor attacking the horn, everyone uses poison potions. The Animated Horn and it's Sattelite Horn spawns will use Horde Lullaby, and without these you'll definitely lose. The fight has a time limit, which is based on the Animated Horn's interest in fighting. This fight is tougher than other Animated Weapons, becuase the horn has no Relic Weaponskill to keep it's interest - however, it's rumored that Light-based relic weaponskills will extend the Horn's interest. If the Horn becomes too disinterested, it will cast Warp on itself and the fight will end. A Burn-type strategy is essential.
Begin the fight by having all available BLM's time their highest nuke spell to hit Animated Horn simultaneously, from max casting range. It will immediately spawn Sattelite Horns, at which time your main PLD/War tank should Provoke the Animated Horn and Invincible, pulling the main horn to the camp. Sattelite Horns should be either ignored or sac-kited by a single person with an AOE away from the main group. All melees should be using any Damage Dealing 2hr ability as soon as they're engaged, except NIN; and all mages should also use their 2hr abilties if it will improve their Damage over Time (Chainspell Tier 3 nuke), except SMN - they can use their avatars (preferably Fenrir) and use Astral Flow, but not the bloodpacts yet - you do NOT want any extra adds in this fight, and you'll only get off one bloodpact anyways. You will have about 30 seconds before the horn loses interest and begins to cast Warp - this is when NIN's will Mijin Gakure and SMN's will use their Astral Flow bloodpact on the horn, in an attempt to finish it off quickly.