Combination Attack: Advance marks the first appearance of the Final Dynamic Special.
Expy: Almost all original mecha in Advance are cut-and-paste copies of the original machines from Super Robot Wars 64, which led to Wild Mass Guessing by fans the 64 and Advance stories are interconnected, which was Jossed by Word Of God.
However, the Super Robot Wars 64 plot does share similarities with the Super Robot Wars Advance backstory (The goals of the Original Generation villains of both games is fundamentally identical, along with the protagonists of Super Robot Wars 64 ending up as a heroic Shadow-Mirror equivalent) along with a Gespenst MK-III reference. And considering how Terada treats the fanbase...
Foreshadowing: The mention of a Gespenst MK III in Advance paved the way for a certain rivalry Axel fuels in the Original Generation sub-series. Unfortunately, this only sets him up for a massive Flanderization that displeased the fanbase. It takes an Updated Rerelease to set things right.
It also mentions "W16", who certainly doesn't appear in Advance but in Original Generation, the character's given the name "Echidna Iisaki"
The Gespenst MK-III was also mentioned in the Super Robot Wars 64 backstory.
Guest Star Party Member: In the Earth route for scenario 8, Schwarz Bruder appears to help you at level 10, with some incredibly overpowered stats and all six Spirit Commands at his disposal. Due to what you'reup against, he's more than crucial.
Also Sayla Mass: she joins you in the early Space Route for several missions...then she leaves...forever
Heroic Sacrifice: Richter and Raiza, though not by throwing themselves into the sun like how Richter did it in the original series, but blowing themselves up in a nuclear level explosion, wiping out half of the army of the Vegan Alliance.
Subverted in the case for the chosen protagonist, who fails to kill the Big Bad by self-detonating his/her machine
Hey, It's That Voice!: Particularly in Advanced Portable: Both Nobutoshi Canna (who HAD to record Silly Axel's voice (because he didn't go silly in OG); also recording Axel vs Vindel and Axel in the Vysaga) and Kaori Shimizu return.
Karma Houdini: No, no, no. If you really want to kill Haruki Kusakabe, wait until future SRWs. But at least you screwed his plans up so much there's no way he can carry out the Prince of Darkness plots.
Made of Iron, No One Could Survive That: This explains why Axel/Lamia survived after self-detonating their machines to protect the heroes. If this doesn't impress you, how about surviving after being punched by both Domon Kasshu and Kazuya? For Lamia, she gets hit RIGHT AT THE VITALS and shrugs them off just fine, though relatively justified since she's an android, but for Axel, he manages to stay on his feet, clutching his stomach. It's later revealed Domon and Kazuya BARELY missed his vitals; Axel vaguely dodged it by reflex.
Mid-Season Upgrade: One of the few instances in SRW where it's averted: Axel and Lamia's starting machine gets upgraded in no way, shape, or form. The closest you get is unlocking the mecha's final attack when they hit level 20, but Level Grinding can get you the attack quite quickly.
Nintendo Hard: Even the original game was pretty tough, but Advanced Portable was made even harder. In particular, the Random Number God who presides over Fire Emblem wandered in and is now out for your blood.
Pink Girl, Blue Boy: The exclusive Super originals: Axel gets the blue Soulgain, Lamia gets the pink Angelg.
Real Men Wear Pink: If you play as Axel, you'll see Shadow-Mirror mooks riding in Lamia's really girly Angelg in the last few scenarios.
The Rival: Whoever the player doesn't select as the protagonist becomes the chosen protagonist's rival for the duration of the game.
Minerva X/pilotable by any Mazinger universe's character (recommended for Sayaka, since this mecha was originally destined for her...and you can finally team her up in special double attacks with Kouji/Mazinger as true both pilot and mecha partners)
Shout Out: Amuro Ray in the Shadow-Mirror universe died in the Battle of A-Baoa-Qu. This certainly sounds familiar in a certain Gundam novel.