The Ending
Warning: This contains large Spoilers!
Zidane learns that Kuja was his brother, and that he was born on another seperate planet where a man named Garland seemed to rule. Kuja kills Garland eventually in his power struggle. Zidane goes to this other planet, of course. Here, he defeats Kuja. There's some more adventurous stuff going on, and then they go to a place known as Memoria. They fight Kuja again here,  and then defeats Necron, this huge super-hard boss. Here is what he's like:
Necron
HP: About 60,000
MP: Enough to last him the entire battle
Attacks: He has a lot of attacks, some that make the entire party get infected with ALL the status effects (including Death or Zombie) or another attack that reduces the entire party's HP to 1.
Strategy: Cast Tent on him to have Poison/Darkness on him. Make sure ZIdane trances, keep Dagger or Eiko to cure everyone. I had Zidane, Dagger [Garnet], Steiner, and Vivi. I had their HP's all above 4000! This is almost necessary. Just carve away on him until he's gone. I suggest Zidane's trance and then do the 9,999 attack 3 to 4 times. A MUST!

Afterwards, Zidane and party begin to board the Invincible before Memoria (above the Iifa Tree) blows. Zidane, though, decides to stay behind. A tearful Dagger watches from the Invincible as Zidane remains (he wants to stay with his brother Kuja, whom is dying).
Zidane goes to Kuja, and the Iifa tree seems to crush them from the inside. The game speeds forwards to Dagger, about 2 or 3 years later, inviting the party for a reunion (except the missing Zidane, of course). At the reunion, they watch the play " I want to be your Canary", this time honestly performed by Tantalanus. Throughout the play, one of the actors - 'Marcus'-is in a robe. Suddenly, at the end, the character turns towards Dagger in the balcony and professes his love for her. The robe is thrown off - - it's Zidane! Dagger nearly dies of shock (below).
Garnet/Dagger runs towards Zidane on the stage, throwing off her jewels and crown as she goes - giving up her riches for her dear thief. She collapses in his arms, crying in frustration, and then they passionately embrace...
Thus Ends The Tale
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