Since most of our answers are the party can win. If the goal is to have the Dragon win (or just make it really hard), break out the Dragon spellcasting rules.

An Adult Red can cast up to level 5 spells. Invisibility, Mirror Image, Wall of Fire, Greater Invisibility all come to mind. I can easily imagine the Red sneaking up on a group of adventurers in its territory with invisibility on. It opens with a surprise Wall of Fire to corral its prey. In the first real round of combat it separates the strong from the weak with a good old fashioned Fire Breath. Next round it picks a tasty target, tenderizes it with a claw attack, grapples it with a second, flies it through the Wall of Fire to get a little extra searing on the tenderized meat, and then bites down to try out its meal.

You get the idea...