the Legacy Advantage was found from a word search located in the Your Headmasters thread. The words you searched for needed to be reordered to spell a clue that told you to send the word search to "mom" and say the magic word. mom = Teruteru's Mom .
idol 1 was hidden in the supreme leader challenge. the fakeout form had a clue in it that asked you to use the letters from part 2 to spell the name of a legendary deceiver (loki) and pm it to the mods
idol 2 was hidden in labors of kirumi. there were hidden monokuma images in each of the hyperlinks in the challenge. the very long monokuma theater contains a hint to this effect, but nobody noticed that
With view source/inspect element allowed in the challenge the real trick is probably to spam your forum full of image links and the words "imgur" and so on, or else someone can set posts per page to 100 open all the threads inspect srouce ctrl-f "imgur.com" and nail ya. If you post hundreds of images that strategy won't save so much time.
although you won't need it anymore because I just used your account to check and make sure it worked when i turned off showing edit notes to non-staff just now <_<
Remnants of Despair (pink) has a good strategy. 30+ pages of threads all with the same name and all with a lot of fake imgur links in spoilers. I'm not gonna root around in the threads because I don't want to affect the # of views but green will have to have put hundreds and hundreds of imgur links in all their posts for their item to be as hard to find as pink's