The achievement for the first victory in the fire raid can only be obtained in the group raid, since that's the only raid you can do at first. The solo raid is only available after several victories, so the achievemnt wasn't added there. I assume you have a save file from before the achievements were added, and that's why you "skipped" that part.
Not all equipment can be obtained by assembling parts. There are also a few class related armor pieces, where you can only get 1 of 2 based on which class the character has.