Why didn't Melody (センリツ, Senritsu) enter Greed Island and use the Angel's Breath (G.I card) to heal all the after effects (her arm, figure etc. etc.) of the Sonata of Darkness that she listened to ?
There's really no indication that Melody even knows that the game exists.
While the Greed Island game is among the easiest "treasures" to acquire in the Hunter x Hunter world (it's ranked in the second lowest difficulty tier, and only because it's so expensive), not every hunter knows ever item that exists. There's really no indication that Melody has ever even heard of Greed Island. Even during the Yorknew City arc, when the auction for a copy of the game in an auction, Melody was busy doing her job as part of Killua's team.
Afterwards Melody wasn't really seen in the story until the Succession Contest arc. I haven't read it yet, but I don't think Greed Island played any part in that any more.
There's also no indication that items inside Greed Island are public knowledge.
Sure, the people playing the game have a pretty good idea what all is in the game (and the people hiring them). But outside the game nobody has mentioned any item that's in there. So, even if Melody had heard about Greed Island, for a rumor or something, there's a good chance that she'd have no idea an item like Angel's Breath would be in there.
Before the details of Greed Island were introduced to us as readers, all characters did seem to consider it as just some regular-ish game. A rare and unique game, but still just a game.
That might kill you for real.