[MENTION=6958799]Karsten Crump[/MENTION] Based on your red dragon hatchling stat block, I'm assuming your party is comprised of low-level PCs.
What I've done in a similar scenario is treated the dragon as not so much a monster, and more as an event steering the adventure. For example, a red dragon attacks a fortified old town/freehold with labyrinthine streets built atop one another and several marginalized classes of people living in slums. Let's say the red dragon's motive is revenge, pure and simple. Maybe it thinks the Lord's son destroyed its eggs which are only lain once per century (indeed, there could be more to this story).
You don't give the party the suggestion to "kill the dragon." No NPCs expect the low-level PCs to do that. This is an honest to goodness adult red dragon, let's say. At most, with intelligent defenses, rallying the population, and some creativity, the PCs might be tasked with repelling the dragon. Create a rough timeline of the dragon's attack, its strategy, how the defenders respond (or fail to) without the PCs intervention. I could see fire being an ongoing hazard, maybe lighting barrels of oil, pitch, or whale fat on fire, creating lakes of fire on the river or at the port. Maybe buildings collapse, giving an opportunity for escape / rescue / exploring the old undercity. Maybe there is a slum at high-risk of becoming a preferred target of the dragon due to the Lord's callous/careless defensive strategy of his keep. Maybe there are hard-edged NPCs (thieves' guild?) who are reluctant to provide access to their secret smuggling tunnels despite the threat of the dragon. Heck, maybe while ascending a tower to reinforce the beleaguered arbalasters, the PCs can hear the dragon monologuing as it flies outside the tower or peers through arrow slits (which the PCs can communicate through...and the dragon might shoot a gout of flame through (this would only deal a few d6, not its full breath weapon).
That's how I would frame it. Success is driving the dragon away, NOT killing it. Thus success need not be measured in damage dealt; in fact, the PCs themselves may never make a single attack roll against the dragon.
Maybe the PCs later hunt the dragon down to kill it and take its hoard. Or maybe they discover who really destroyed the dragon's eggs, and cut a tentative truce with the dragon to help it bring down the true offender (for a bit of its treasure). Or maybe the make the dragon see the err of its ways (e.g. making scorching the town to cinder too costly / discovering that the Lord's son couldn't possibly have destroyed the dragon's eggs) & it issues an ultimatum to deliver the guilty person in 1 month or it will return to finish what it started. Or maybe the town burns, and success is measured in how many are saved & how much the PCs learn about more pivotal plot points. Or maybe they launch a coup against the Lord and his foolish son, and turn the offending nobles over to appease the red dragon.