Giant Eagles are dangerous birds, bigger than grizzly bears but with one additional advantage - they can fly. They appear in savage mountain areas. Like most wildlife, they tend to stay away from your dwarves, but if they do come close or are harassed by hunters or soldiers, fun may ensue.
Flight enables the giant eagle to fight beyond the reach of melee weapons, hovering to swoop in again and again to pick off dwarves that stray from the pack. Furthermore, Giant Eagles show a tendency to avoid any dwarf armed with a crossbowVerify, rendering your best chance of killing it that much harder. It's always possible for any dwarf to get a lucky hit, but it's not something you want to count on.
Should your dwarves be unfortunate enough to encounter a skeletal giant eagle, which is immune to the worst effects of piercing weapons (like crossbow bolts), you may want to consider abandoning your fortress and starting a new one far, far away. To witness its cruel devastation may scar you for life.
Giant Eagles can be caught in cage traps, however this is extremely rare. A much easier option, although not quite as profitable, is to buy them from the elves. If they are caught, they can be tamed, and having a giant eagle hovering outside your base is an excellent defense mechanism. Watch as it ignores your stay inside orders, and utterly destroys your enemies.
One way to cheat your way out of a sticky situation is by modding the eagle entry. Wait for the bird to fly in the air and then save your game. Open the raw/objects/creature_large_mountain.txt file and delete the [FLIER] tag from the Giant Eagle. Reload your game and enjoy watching the bird plummet to its death. (Note that if it survives, or any new ones spawn, they can still attack your dwarves!)
[CREATURE:BIRD_EAGLE_GIANT] [NAME:giant eagle:giant eagles:giant eagle] [TILE:'E'][COLOR:6:0:0] [MODVALUE:5] [LARGE_ROAMING][DIFFICULTY:2] [FLIER] [GENPOWER:3][LARGE_PREDATOR][NATURAL][PET_EXOTIC][MOUNT_EXOTIC][SAVAGE] [PETVALUE:700] [PREFSTRING:coloration] [BODY:HUMANOID_ARMLESS:2WINGS:2EYES:2LUNGS:HEART:GUTS:ORGANS:HUMANOID_JOINTS:THROAT:NECK:SPINE:BRAIN:4TOES:BEAK] [SIZE:10] [MAXAGE:10:20] [ATTACK:MAIN:BYTOKEN:BEAK:bite:bites:1:6:GORE][ATTACKFLAG_CANLATCH] [CHILD:1][CHILDNAME:giant eagle hatchling:giant eagle hatchlings] [FAT:3] [ALL_ACTIVE] [BIOME:MOUNTAIN] [STANDARD_FLESH] [HOMEOTHERM:10067] [LAYERING:100] [SWIMS_INNATE][SWIM_SPEED:2500]