Kirameki Project

Junerin looks smaller than she actually is. Front row: Nene, Kana, and Kroné. Back row: Rincle and Junerin.

Kirameki Project starts with an unprovoked attack by a Humongous Mecha against a German mecha squad - the attacker defeats them all and takes their national emblem, adding it to a collection. We then shift to Genes, an idyllic and technologically-advanced Mediterranean island nation governed by three princeses: Kroné, Kana, and Nene. The mecha from the earlier attack arrives at Genes, looking for a fight... but Kana is reluctant to send out her giant robot until Nene's life is endangered.

Kirameki Project is a five-episode Super Robot OVA anime, produced by Studio Fantasia and released in 2005. The series was directed by Katsuhiko Nishijima, who had previously directed both Gunbuster and Agent Aika... and both influences show in this work.

If it's on the Mecha Tropes list, it's probably parodied here. Other tropes used in Kirameki Project include:

Action Girl: Nene so desperately wants to be one, but she ends up either a Badass in Distress or a Faux Action Girl instead, depending on the circumstances.
Berserk Button: Wholesale destruction isn't enough to motivate Kana, but so much as scratch one of her girls...
Combining Mecha: Rincle and Junerin combine with Kana in the pilot's seat during the final battle with The Perfect. This may be the only time in any anime where we see a Humongous Mecha Meganekko.
Conspicuous CG: All of the giant robots are obvious CG, and everyone else is illustrated in a traditional cel-shading style. This trope comes into play when both humans and robots are in the same scene.
Flying Brick: Nene has power of flight, super strength, and near invulnerability when she wears the "Powered Suit" created for her by her Wrench Wench sister Kana. This being a Studio Fantasia work, Nene's suit also serves to make her a Fan Service object.
Genki Girl: Rincle, especially in contrast to The Quiet One Kana who she's usually seen beside.
Handbag of Hurt: It's not just a fashion accessory for Junerin. It's later swapped out for a Parasol of Hurt.
Humongous Mecha: It wouldn't be a mecha show without them! Big Mighty, Junerin, The Perfect, and some unnamed giant robots all appear.
Informed Ability: Played for Laughs with the Kroné Rose Knights. They're called the last line of defense of the kingdom, but circumstances conspire to prevent them from actually doing anything other than be forced to throw a fight.
Macross Missile Massacre: Launched against the Flying Brick by the Big Bad's mecha.
Meganekko: Kana (voiced by real-life meganekko Mai Kadowaki).
Most Common Superpower: Nene, who uses it for a Marshmallow Hell attack during one episode.
Older Than She Looks: Kana looks to be the youngest of the princesses (being mistaken for a 12-year-old by Ooya at one point), but is older than Nene.
Only Sane Woman: Kroné. Luckily for Genes, she's in charge of the military.
Panty Shot: Since it's an anime from Studio Fantasia, it would be faster to list the named female characters who don't get at least one Panty Shot. Even Humongous Mecha Junerin has a few!
Salaryman: Ooya, except that he's traded his briefcase for a giant robot.
Something We Forgot: "I never did get a chance to ask him about this."
The Speechless: Junerin, although she can send emails and text messages to Kana. From Kana's point of view, also a Cute Mute at teh start of the final episode.
Super Speedster: Junerin is eight times as fast as Big Mighty, but only in short bursts.
Swiss Army Hero: Rincle, who has flight, surface, underground, and underwater vehicle modes for Kana to ride in, a special mode useful for cleaning Junerin, and Rubber Man arms. No explanation is ever given for these abilities, they just exist.
Would Hit a Girl: Enforced - if the other giant robots don't at least try to hit Junerin (or Nene), there's no fight at all. Granted, the Big Bad does seem to enjoy it.
Wrench Wench / Gadgeteer Genius: Kana, who built Rincle and Junerin, to whom she's a Mama Bear. She skips school in favor of working on her Humongous Mecha in the first episode.