Honestly? Just use shields. Wooden shields can protect against syndromes and dragonfire. In fact, the only statistic that matters for shield is weight- heavier shields bash for more damage. Addy shields are actually the worst shields you can give your soldiers for this reason (since -only- weight matters) You could also set up a few ballistae ~100 yards down the hall and use those.
personally? I'd bunker him near the start of your fortress and have him toss fireballs at goblins. If gobbo archers get close then drop a bridge cutting off its line of sight. Think "giant cave spider silk farm," but instead with a flaming beast and roasted goblins!

Name him "Torchy" and use him as your mascot. Let him give the elves hugs! The possibilities are endless.
You can't "trap" forgotten beasts, but you can create corridors sealed off by bridges and baited with puppies (put them behind walls so they have ot path forward to get in range). Channel out the tiles adjacent to hte beast room from above, but have a bridge ready to be lowered over said hole to keep the beast from firing on your miner. Then have it wander down the corridors/up the ramps to the puppy bait in your fortification carved/bridge sealed room at your entrance.
I hate simply killing forgotten beasts- its far more dwarfy to bend them to your will, or at least keep them as pets. You can go all "Jabba the Hutt" and have them in a pit under your throne room. You can give out maniacally laughter as you drop other nobles and liasons into the pit! If they have syndromes you can coat your weapons/ammo with it and spread it to enemies. You can also use them as a silk farm, but sadly they have no material modifiers to said silk. Ones made of steel can be used as target practice for marksdorfs with wooden bolts... etc.