How do I unlock rank 4 parts for the Burning Gundam?

Unlock and clear the "King of Hearts' Challenge" Extra Mission. To unlock the mission, you must clear all three "Gundam Fight" Friendship Missions (which are unlocked if your character has cleared 15 or more missions and has a relationship level of "Caution" or below with 8 or more characters), read the terminal message you receive after clearing the "Gundam Fight: Finals" Friendship Mission, and shoot down 3000 or more enemy units while piloting the Burning Gundam (combined total for all pilots). More.

Unlock and clear the "The Final Power" Extra Mission. To unlock the mission, you must clear Shinn Asuka's Story Mode and shoot down 3000 or more enemy units while playing as Shinn. Note that the mission is playable for Shinn only, is restricted to single-player only, and requires that you pilot the Destiny Gundam.

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Unlock and clear the "Burn, Dragon" Extra Mission. To unlock the mission, you must clear Glemy Toto's Story Mode and shoot down 3000 or more enemies while playing as Glemy. This mission is playable for Glemy only, and it requires that you pilot the Bawoo.

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