Final Fantasy VI/Sidequest/Doom Gaze and the Eight Dragons

Deathgaze
The trick to being able to fight Deathgaze is to realize that it isn't a random battle in the usual sense of the word. Every time you take off in the airship Doom Gaze has a fixed location on the world map he is hiding in. To get into a fight with doom gaze all you need to do is find that location and get close enough to it to trigger a battle. Hence, if you're ready to fight, flying around in circles is pointless and wandering around aimlessly may not work too well either. From when you take off, tilt your ship to the right at a very slight angle, then hold L+R to go full steam ahead. You'll move across the map at a slight angle and cover every location until you run into Deathgaze.

For actually fighting Deathgaze, he absorbs most elemental spells, so I would recommend using your strongest physical attacks like chainsaw or non-elemental attacks like Phantom Rush. He's weak against fire and pearl however, so you can try your strongest fire spell or Holy if you have it. And unblockable magic spells like Ultima are always a plus of course. Doom Gaze has 55555 HP total and although he usually escapes before a battle is finished he's unable to regenerate his HP. Meaning, that all you have to do to wear him down is keep fighting him over and over and do some damage each time. And since you know how to find doom gaze with the above method, this should be a cinch.

Deathgaze is vulnerable to the Vanish-Doom (Death)/X-Zone (Banish) combo, but if you use Vanish then Banish, you will not receive the Bahamut esper. There is also a chance you won't receive it when using Vanish then Death. Save your game if you want to be on the safe side.

The Eight Dragons
For all the Dragons you can do the unworthy way of defeating them by the vanish - doom technique. may not always work on skull dragon but try the vanish - life techinque

Earth Dragon
This is the one dragon you won't encounter on any of the normal sidequests. To find it, go to the Opera House, which is in the thin middle section of the left middle continent. Go up to the balcony like you did for the original opera house scene, and flip the second switch from the right to drop down onto the stage. To actually fight the dragon, make sure you have casted Float upon every party member. You can also equip your party members with Gaia Gear which absorbs earth attacks as a better alternative. It's weak to wind and water magic, just use your strongest attacks and take your time and you should be fine.

Storm Dragon
Located in Mount Zozo in Cyan's sidequest. Weak against fire, absorbs Thunder magic. 42000 HP total.

Red Dragon
Located in the Phoenix cave in Locke's sidequest. Weak against water and ice, absorbs fire magic.

White Dragon
Located in a top side room in the fanatic's tower. Equip wall rings on your entire party as usual in the tower. It absorbs pearl magic and has no weaknesses, use unblockable spells like Ultima or your strongest other magic.

Blue Dragon
Located in the secret room in the ancient castle in Edgar's sidequest/Ancient Castle. It is weak against lightning, use your best physical or magical attacks as usual, and you should have the offering to help you out a lot.

Ice Dragon
Located on the snowy hills of Narshe where you fought Kefka, in Mog/Umaro's sidequest. Use your strongest fire magic and it absorbs ice naturally.

Gold Dragon
Fought by your second party in Kefka's Tower. Attacks with lightning, weak against water, by this point you should have enough powerful magic and attacks to finish it.

Skull Dragon
Fought by your third party in Kefka's Tower. An undead dragon with annoying status altering spells. Ribbons help naturally, and use your strongest fire spells or Holy.

Afterward
After defeating the eight dragons, you will receive the Crusader (Jihad) magicite. In the Game Boy Advance version, a small tablet will appear in your inventory telling you to go to the "Dragon's Horn". The "Dragon's Horn" is located above the Dragon's Neck Coliseum.

Needs the usual template for bosses and a good deal more info+pictures.