This is Final Fantasy: Legend of the Crystals (1994).
Final Fantasy: Legend of the Crystals, released in Japan as Final Fantasy (Japanese: ファイナルファンタジー, Hepburn: Fainaru Fantajī), is an anime OVA based on the Final Fantasy series of role-playing video games. It was released in Japan in 1994 and distributed by Urban Vision across two volumes in 1997 and 1998 in North America on VHS.
Based on the obscure "Final Fantasy 5". 150 years later, two decendants of the heroic Battsu must track down the crystals. Along their way, they meet monsters, phantoms and two airship captains, one a bumbling yet ambitious man and the other a sexy pirate leader.
The story features two protagonists: Prettz, a young man who wields a samurai sword and wears red chest and shoulder armour, and Linaly, a blue-haired young woman in mostly purple garb.
Early in the story, they're chased by a pink airship manned by the captain of the sky pirates, Rouge, and her all-female crew.
The duo subsequently make their way to the Temple of the Wind, where they find the Wind Crystal, which enters Linaly's body through her chest and remains inside her.
After that, the duo is confronted by Commander Valkus, who lands near them in a blue airship. They manage to elude him but are captured by Rouge and her sky pirates and placed in a prison cell.
While they're in the cell, the Wind Crystal emerges from Linaly's chest, floats up near the ceiling, and fires a bolt of energy at the ground, causing the spirit of a boy named Mid to appear. Mid asks Linaly to continue keeping the Wind Crystal within her body, as this prevents it from being detected by the antagonist of the story, Ra Devil, who seeks to acquire it. The Wind Crystal then floats back into Linaly's chest; Prettz attempts to block it with his own body, but it passes through his torso and back into Linaly.
In the climax of the story, Prettz and Linaly defeat Ra Devil, whose body has mutated and grown to massive proportions as a result of becoming the vessel for a monstrous being known as Deathgyunos.