Oh good point, I assumed that was covered by the mini monster recipe note pasted below, but I didn't think of any rewards deeper than that.
"The following Giant Monsters found in city zones now have a 10% chance of dropping an invention recipe of a miniature version of themselves. This chance is rolled individually per character who received credit and is tied to the same drop table as the Reward Merits."
The only other reward on Adamastor was 5 threads for incarnate players, and that was already limited to first time per day (I'm assuming it was 18 hour, also).
I still can't think of any deeper rewards off the top of my head. I don't think it applies to badges, but it would suck if you went and got rewards other than the defeat badge (by your character/team not doing 10% or more damage) and then defeated another one and qualify for the badge but not get it. (Like multi spawn Titans when nobody bothers to invite the lower levels; so I'm glad that Titans are not on an 18 hour cooldown in this use case.)
First defeat of Adamastor gives:
[14:37] You received 10 units of Reward Merit.
[14:37] You received 6 units of Reward Merit.
[14:37] You received 5 units of Incarnate Thread.
[14:37] You received Monstrous Aether.
I'll have to wait until it can be summoned again before I can tell you what the second defeat within the 18 hour cooldown gives.
*Edit:
[16:19] You gain 51,000 experience and 17,000 infamy.
[16:19] You received Monstrous Aether.
Not sure if the Aether was intended to be rewarded if the Reward Merits are not, but there you have it.
No threads nor Merits if the 18 hour reward cooldown is still in effect.