So these quests are probably going to be a little long. Lost FILL CANNON is long because it forces you to clear the CCA areas one at a time, much like Lost DEVIL'S SCEPTER did. Lost CHARGE VULCAN is only one Tower but some floors are difficult, especially 10F.
Monster counts are below. Note that each quest has some spawns that require multiple players to trigger, and Lost CHARGE VULCAN's monster counts are vastly different if you're playing with less players. The count below is a full clear which will require four players. For example, if you were to play the quest in one person mode, you would miss out on at least one spawn on more than half of the floors.
Also make sure you talk to Paganini next to the main warp to Tower I'll probably change the quest so that you can't go to Tower until you demonstrate you understand what Paganini said. I should probably get a translated version of the quest up as well.