Cecil is faced as a boss three times in Final Fantasy IV: The After Years. He is fought in flashbacks in the Lunarian's Tale, and in the main story in the final tale, The Crystals. The battles are scripted and for story-telling purposes.
Lunarian's Tale Edit
The battles featuring Cecil are scripted and cannot be affected by the player. In the first battle Cecil will attack Golbez twice, and on the third strike instantly kills Golbez. The player can acquire a unique weapon for Golbez, the Ebony Blade, by opening the item menu before Cecil kills Golbez and pressing to view Golbez's equipment, then un-equipping the sword so it will appear in the inventory when the proper tale begins.
At the end of the tale, the player faces Cecil with other party members in two flashbacks. The player's actions in both flashbacks are meaningless—they cannot do enough damage to kill Cecil or his allies, and they will not do enough to kill Golbez, and eventually the fights end in story sequences.
The Crystals Edit
Cecil will face the party in scripted encounters in cutscenes as the player progresses through the tale. For the eventual true fight, he will summon Odin to aid him, but Odin will not attack. Cecil will only use physical attacks, but they can be quite powerful.
After several rounds of fighting, Odin will speak and then turn on and defeat Cecil, ending the fight. It does not matter if the player focuses on attacking Odin or Cecil, they merely need to fight and stay alive until Odin comes to his senses.
Cecil is fought one last time in the ending sequence, being fought with just Ceodore. Much like battles in the Lunarian's Tale, the battle cannot be lost or won, and will end automatically after a few turns.
Rosa and Kain can buff the party with Blink and Protect, and if he is at a high enough level, Ceodore can also use Blink. Together, the three can keep Blink status on the entire party and stay protected from Cecil's blows.