These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Breath of Fire I
Game Breaker: The Agni transformation makes the game incredibly easy. Merging the whole party into a single being, max HP, an attack that does 999 damage, and status immunity would do the trick.
The (Boomer)Rang weapons. Combine them with Mrbl1 items (a cheap, easily obtained item that guarantees Critical Hits), and you will wipe the floor with the entire enemy group with just Ryu.
For that matter, Mrbl1. Just Mrbl1. These also work on Ryu's dragon attacks too. Carry entire stacks of these around, and bosses die much faster. Well, until you get Agni.....
Karn's fusion forms are similar. He combines with two or three other party members for a major stat boost. He'll always go first and will deal more damage than anybody except Ryu's dragon forms and Bleu's magic. Unlike Ryu's dragon forms, Karn's fusions aren't limited to one fight, so unless you need a map ability, there's little reason not to have him fused.
Tear Jerker: Cerl and Alan's ultimate end, definitively. In The Dragon Warrior manga adaptation, Jade and Sara's final hopeless stand against Myria counts as well.
Although for Cerl and Alan, didn't they get turned back into children due to the Time Key's effects? That seemed to be more like giving her a second chance at life, and allowing her to remake happy memories with Alan.
That One Boss / Wake-Up Call Boss: The Gremlin. He has a ton of HP and will start spamming a powerful group-hitting attack when his initial health bar runs out (at which point his HP is only about 1/4 to 1/3 of the way gone).
That One Level: Most of the surreal dungeons on Mote's dreamworld, the crystal-path maze being specially loathed.