Badges of Honor Legendary???
I don’t think so. Unless you want to gamble with the Mystic Forge the only progression towards a legendary from badges that I’m aware of is the Gift of Battle.
The rest of your badges can be spent skins (one of the best uses of badges), armour and siege (but it’s so cheap on the TP now).
You can convert badges to gold by buying seige and the TP’ing them.