Like most Level Breaker fights, Raubahn may give up before he is defeated.
Raubahn has access to all Blue Magic spells at and below level 70. Which spells he chooses to cast is completely random. Be aware that he casts all spells within 1-2 seconds as opposed to their normal casting time.
Unfortunately, the outcome of this fight is usually determined by which spells Raubahn chooses to cast. Higher-tier, damaging spells will usually kill the player, whereas support magic, even Magic Fruit, will afford the player the opportunity to deal damage to Raubahn.
Raubahn may use Azure Lore, and appears to be more likely to use it if the player does.
Beware of casting any HP recovery blue magic on yourself other than Plenilune Embrace (which is only available if you are attempting this fight at a high level just for fun). The casting times are too long and the HP recovery too small for other healing spells.
A common strategy for this fight is to use as many damaging spells as possible in order to defeat Raubahn before he defeats the player.
Spirits within strategy: Use an icarus wing and opo-opo necklace to get to 300% or close to it. Sleep Raubahn with Yawn, then dispel his cocoon and stoneskin. Engage and use Spirits Within which will do massive damage relevant to your HP (HP food/gear helps), most likely 1000-1300 damage. At this point you have almost won, simply cast a couple of DD spells and the fight will be over. This is pretty much a guaranteed very easy win.
Many players agree that opening with their highest tier (and slowest) Breath Damage spell (Frost Breath) outside of Raubahn's aggro radius is highly effective. A full HP/MP set will allow this spell to do high damage and effectively make it costless when you switch to your normal DD gearset.
Another alternative for 75+ BLUs is Azure Lore, Convergence, Bad Breath, which will inflict a potent paralysis and possibly other effects on Raubahn. This strategy is not available unless you have already completed another level 70 limit break quest and are level 75 or higher with 1 or more merits in Convergence.
Cannonball is another useful spell that can be cast outside Raubahn's agro radius/spell-casting range.
Once in range, fast-casting Physical Blue Magic spells, as well as Head Butt, make short work of Raubahn.
Because of the quick nature of this strategy, job traits and spells geared around "endurance" will not be particularly useful. There is also no need to set recovery spells such as Magic Fruit.
An alternative strategy is to employ a Sleep/Bind/Nuke strategy (with appropriate gear), similar to other Mage Level Breaker battles.
Raubahn is susceptible to the effects of Sheep Song and Yawn, giving the player ample time to recover, wait on recast timers, or even wait out his Azure Lore. Yawn is a gaze-attack, so Raubahn must be facing you for it to connect. Beware of using spells with Damage Over Time effects when employing this strategy!
Regurgitation inflicts both damage and Bind with a large range (~22 yalms) and relatively low MP cost, making it a highly useful spell for this strategy.
It is possible to SilenceRaubahn with Chaotic Eye, leaving only his standard attacks and weapon skills. However, his sword is guaranteed to be deadly, but if you're lucky, he may use spells that aren't devastating. Do not attempt to silence him. Furthermore, Bad Breath with Azure Lore and Convergence active did not silence him, but did inflict a potent paralysis.
It is possible to AspirRaubahn with MP Drainkiss. However, it is not practical to cast MP Drainkiss. Most likely, before MP Drainkiss has been cast, it will be either interrupted, and then you will die, or you will die even before it's interrupted.
Blank Gaze, Geist Wall, and Frightful Roar all do zero damage and can be used while Raubahn is sleeping without waking him up. Putting him to sleep and dispelling him before doing a majority of your damage is recommended.
A mixed strategy is also possible, employing some of the damage-dealing capacities of the first and the enfeebling effects of the second. The use of elemental staves will greatly enhance the accuracy of your magical spells, but is not fully necessary. Beware that because Blue Mage has no native Staff Skill, you will need to switch to a sword whenever you cast physical Blue Magic. Switching weapons will also remove your TP.
The least expensive route to go is to simply Opo-Necklace to 100% TP. Then buff, rest, and open with Frost Breath. Then cast Head Butt, 2 DD spells, Head Butt, repeat. Bring an Echo Drop, just incase.