First off -- this differs from our history questions on this topic in that we are dealing with modern assets here, not historical ones, and from this question in that our military units are out to slay the dragon, not recruit and utilize him. Furthermore, we are discussing tactics and strategy here, not the level of technology needed.
In the left corner, we have our big, scaly, fire-breathing, livestock-chomping dragon. He's been kept alive throughout history by scales that can stop blade, arrow, bolt, and anti-personnel bullet, up to a ordinary slug of 23mm caliber and armor-piercing slugs short of 12.7mm caliber. He has human-like intelligence (if not better) to go with nasty, albeit short-ranged, fire breath and quite the appetite, as well as the ability to extract energy efficiently from most organic carbon sources (so he can dine on trees just as well as cows or princesses). His flight envelope is similar to a small aircraft: +4 to -2g, with a max cruise speed of 75 knots and a max dive speed of 150 knots. He also needs to sleep at least 4 hours per 24 hours of wakefulness, and cannot do so on the wing.
In the right corner, we have a Marine Expeditionary Unit -- the smallest complete combined-arms fighting force in the United States Marine Corps. This MEU has but has one mission -- slay the dragon, and they must do it on their own (i.e. no reinforcement units allowed). Our modern-day dragonslayers do have an amphibious assault ship's worth of ammunition, fuel, and supplies available to them, as well as the ability to obtain food from the land and purify the water sources available to them, and utilize any liquid fuel stores that have been left behind in the land.
Furthermore, this battle is taking place over mixed terrain (wide elevation, temperature, and moisture variations) in a 500km square area. Basic roads are the only fixed transport assets available on it (i.e. no divided highways, aerodromes, or dedicated port facilities), and the civilian population is sparse (most of them have fled the dragon's ravages already), so civilian casualties are not a major concern.
How can our MEU's commander best accomplish his mission? (I.e. most expeditiously and/or with the fewest casualties)