1 chest right at the start, can solo just wipe and check first door on the left to see if it's there. Potentially gives exotic weapons, usually radiant shards/energy. First thing I do when I get on after a Tuesday reset

1 drop at the end of the abyss after forming the bridge, can give armor / shards / energy. Can solo on any character, invisible hunter is prob easiest. Use "rock / lamp jump" trick https://www.youtube.com/watch?v=LbrWT9eF7eo to make it doable on other chars that aren't invisible.

1 drop at the end of the next stage, swordbearers / form the bridge. Can give armor / shards / energy. Can solo easy with a resurrecting warlock using cheese, other classes bit harder. need to snipe loads of enemies on the far side until ogres come, then snipe those too. or can fly across with sword tricks. can even do it legit by carefully managing the bridgeforming stage, backing in and out so as not to get annihilated.

Secret chest after the next short corridor, can give energies / shards. Need to make it in under 60 seconds from the start, and quick once killing the final shrieker / entering the room or the door will close. probably very hard solo, but with a team can leave one there to revive others and swap in all alts. despawns after maybe 8 minutes.

Nothing for the Deathsinger as far as I know.

Final drop after beating Crota, can give armor / exotics / raid speaial or heavy weapons / shards / energies. Can be soloed by a 32, with exceptional skill. Prob only really doable with a team.