Ace Pilot: Minoru and Jonathan aren't bad pilots per se, but they're still overshadowed by Hawkeye.
Arranged Marriage: Vergil is arranged by his family to marry Rosaly ,heir of the Vritania Company. It doesn't go well for him.
Asshole Victim: Hisui. Sure, the way that she was killed is horrifying, but given that she was a mole for the Vritania Corporation, and lured Minoru and his teammates into a trap, no one mourned her after her death.Also, Kyle and Rosaly are killed by Chakal towards the end
Chakal Hazard is a popular singer and actor, and is the reason why Lucia becomes a Idol Singer in the first place. Eventually, she discovers that he is the responsible for her mother's death, and consequently, her conflict involving her family.
For Vergil, there's Rosaly Vritania, heir of a famous company. She is also his fiancée and also motivates him to be "the best". Not only Rosaly is cruel and hateful towards everyone, but the Vritania Company is also behind the Alien Invasion.
Culture Equals Costume: Lucia loves to invoke this trope during her shows. Her planet, Madlirosa, is already a Fantasy Counterpart Culture for both Mexico and Spain, so, naturally, expect her with a red Flamenco dress and Calacas (Mexican skulls) in her backgrounds. Or a sombrero and a poncho.
Minoru, Hisui and some japanese characters were raised on planet Yamato, the equivalent of Japan.
The planet of Aeropa is one to the Europe as a whole.
Kid Detective: Clara. Although she is more like a teendetective.
Happily Adopted: Clara was adopted by Haddock when she was a kid.
Hollywood Tone-Deaf: Clara is a terrible singer. Her tone-deafness is a major Running Gag in the anime, given that in every episode that she appears, Carla wrecks a karaoke box with her singing. Which is actually one side-effect of Clone Degeneraton.
Clara means "clear", but also is connected to the word "light", a hint that she is a clone of Lucia. Her surname, Sherlock, is a reference to Sherlock Holmes. Fitting, since she is also a detective.
MegaCorp: The Vritania Company, led by Kyle and his sister Rosaly.
Missing Mom: Lucia's mother. She was killed by Chakal after she refused to marry him.
Named After Somebody Famous: Minoru Akatsuki is named after Minoru Genda, a famed Japanese military aviator.
Ring of Power: Lucia have one in her ring, given by her mother before leaving. It's made of Orichalcum, a metal which is connected to the aliens.
Thinks Like a Romance Novel: How Vergil sees his relationship with his fiancée Rosaly. Let's just say that Rosaly kicked a few puppies during her career.
Your Days Are Numbered: Clara only has few years to live, given that she is actually a clone of Lucia.Thankfully, she outlived the life expectations.