The Subspace Emissary depicts two realms: The "main realm" of "our world", known as the World of Trophies and is very much a typical Earth-like setting, and the realm of Subspace, a world of darkness. The "master" of the world of Trophies is the entity known as Master Hand; likewise, Tabuu, the main villain of the plot, is the master of Subspace and the effective embodiment of it. Tabuu intends to cut the World of Trophies into pieces and assimilate them into his own world. In preparation for this plot, he has long observed Master Hand and the fighting denizens of the World of Trophies (hereby referred to as "Smashers"), studying the fighting styles and mechanics of the trophy-based characters. Tabuu himself cannot leave Subspace, so his plan is to gather and arrange an army that Master Hand would lead as his proxy.
Tabuu captures and enslaves Master Hand, and bends him to Tabuu's will using chains of light. Very shortly after acquiring Master Hand, Tabuu learns of the Smasher named Mr. Game & Watch, an entity without any concept of good or evil but is comprised of a trans-dimensional "mass" that has strange qualities. An infinite amount of a primordial substance known as Shadow Bugs can be extracted from the Smasher, so Tabuu and his puppet Master Hand capture him for themselves. Using the Shadow Bugs, Tabuu creates much of his Subspace Army, the force which he will have his puppet Master Hand command to invade Master Hand's own world in the plot to bring it into his master's world.
The next phase of Tabuu's preparation for the operation to assimilate the normal world into the world of Subspace centers on the Isle of Ancients, a mysterious landmass that floats in the sky above the World of Trophies. The society within the floating island is filled with advanced technology and is populated by a group of sentient robots classified as R.O.B.s, and they have existed for an indeterminate amount of time without any interaction with the civilizations on the landmass below. The hierarchy of this society is comprised of lesser R.O.B. minions serving one R.O.B. known as the Master Robot with complete loyalty, and they have all lived in peace... up until now.
Tabuu's Master Hand-led forces take the Isle of Ancients hostage, and the Master Robot and its R.O.B. brethren are blackmailed into agreeing to be the main front of the Subspace offensive. The R.O.B.s thus begin to develop and produce the various armaments and utilities to be used by the Subspace Army, including primarily the Subspace Bombs, the timed devices that would explode to engulf a massive portion of the world into a pocket of Subspace and send that part of the World of Trophies into Tabuu's realm. Each bomb would be deployed by the Master Robot himself, and two R.O.B. minions would plug themselves into each bomb to set its countdown timer, which would essentially result in the sacrifices of each R.O.B. unit once that bomb detonates. The Master Robot, out of shame and sorrow for his decision to serve and further Tabuu's scheme for domination and how this is sealing the fates of his brethren, cloaks himself in a disguise and assumes the identity of "the Ancient Minister".
The Subspace Army also takes the plans for the Subspace Bombs and the technology from the Isle of Ancients and begins construction on the Subspace Gunship safely in Tabuu's realm. The Gunship is a colossal airship that can shoot out blasts that fully emulate the effects of a detonated Subspace Bomb; this would be the "ultimate weapon" of the Subspace Army and is Tabuu's intended trump card to complete the operation. But to make this giant airship enter "our world", a massive subspace portal must be made.
In addition, the R.O.B.s develop personal weapons called Dark Cannons, whose projectiles instantly turn any Smasher into its trophy form, thus emulating an ability Tabuu himself holds within his wings (a deadly assault known as Off Waves); the trophification of the Smashers would be Tabuu's intended measure to deal with any resistance they might mount against his operations. These prized weapons are few in number, though, and can only be expected to be used properly by Subspace Army affiliates that aren't just single-minded grunts; indeed, Smashers themselves would best be able to use them. So to bolster the morale and organization of the Subspace Army, Tabuu has Master Hand seek out and recruit Smashers and other high-profile figures within the World of Trophies that would be willing to serve "Master Hand's" operation to assimilate their world into "his" realm of Subspace. Villainous characters that have had personal conflicts with other Smashers in the past are the ones Master Hand successfully recruit, such as Petey Piranha, Porky Minch and Ridley, and the actual Smashers among them are the ones that are given Dark Cannons as the most major members and commanders of the Subspace Army: Ganondorf, Bowser, and Wario.
Ganondorf, a powerful, sinister warlock with aspirations for further power and control, swears allegiance to Master Hand in outward appearances only; his real motive is to usurp power from within and take out Master Hand when the time is right. Bowser, a brutish dragon-turtle-like Smasher with his own little army of grunts and minions, is relatively loyal to Master Hand and likely joins for the sake of settling his long-standing conflict with certain other Smashers, but does not care for Ganondorf. And Wario, a bellicose thug with a penchant for mischief, cares very little for the actual objective he was given and just wants to continue doing whatever he pleases, but he certainly appreciates having a Dark Cannon with which to turn Smashers into trophies. Of course, none of these three Smasher accomplices to Master Hand are aware of Tabuu.
Tabuu's final act of preparation for his invasion of the World of Trophies is the acquisition of the impressive flying warship named the Halberd, owned and piloted by the masked swordsman smasher Meta Knight, as a primary transportation means for the Subspace Army. So, the Subspace Army launches a violent attack against Meta Knight to take the ship for their own. Meta Knight attempts to defend, but by complete coincidence this attack fatefully coincides with an individual assault on Meta Knight by a rival of his, a self-styled "king" among Smashers named Dedede. Dedede unknowingly makes it impossible for Meta Knight to repel the Subspace Army's attack, so Meta Knight is forced to flee and give up his ship to the Army, and hide out in seclusion elsewhere.
Dedede, in the meantime, during his experience with being caught up in the Subspace Army's attack on the Halberd, comes to know all about Tabuu, his true nature and the potential of his Off Waves trophification ability. After he himself flees from the scene, Dedede begins to worry what will happen once all the Smashers of the world are turned into trophies; after all, if every Smasher in the world is reverted to trophy form, there would be no one left to restore them and each other (since characters in the World of Trophies get turned into trophies when defeated in battle but can immediately be restored at any time by an active character hitting their trophy bases), and the World of Trophies would effectively end by Tabuu's hand. Thus, Dedede gets to work on developing special brooches named Dedede Brooches, which are set to work on a timer; after a certain long period of time has passed, whichever inanimate Smasher trophy the brooch happens to be attached to would restore that Smasher to life. Dedede intends to use these Brooches on himself and some Smashers he may find as trophies down the line, so that there is a chance that he and some other Smashers can cheat themselves out of the doomsday scenario that is likely to happen in the near future, and then have a chance to combat it outright.
Tabuu's operation, in the meantime, has fully assembled all its resources and measures with which to commence the official invasion of the World of Trophies to slice it up and send its pieces back to Tabuu's realm of Subspace. With the Halberd serving as the Subspace Army's frontal flagship and effective "dropship", where it would deposit payloads of Shadow Bugs onto areas where the Subspace Army is needed to facilitate each of the Ancient Minister's bomb deployments, the Subspace Army thus begins its campaign.
Lucas is seen walking alone in an area known as the Ruined Zoo (a reference to Podunk Zoo from EarthBound Beginnings), until several Primids show up. Then, suddenly, the gigantic Porky Statue appears and chases after Lucas. Lucas runs from it, until he gets caught on a piece of debris and is about to be crushed when Ness comes to his rescue by attacking the statue with a PK Thunder. Ness blows up the Porky Statue with his PK Flash, which reveals Porky Minch himself (based on his Mother 3 appearance) in his Spider Mech. Ness and Lucas defeat him, but no sooner do they do so when Wario shows up and attempts to shoot Ness with his Dark Cannon. Ness dodges each time, so Wario eventually aims at Lucas and shoots. Ness pushes Lucas out of the way and gets turned into a trophy himself. Terrified, Lucas runs away as Wario cackles in the rain.
Later on, Lucas runs into the Pokémon Trainer as more Primids show up. After they are defeated, the Pokémon Trainer leaves, but Lucas decides to join him after remembering what happened to Ness. Lucas and the Trainer encounter and defeat Wario in the desert wastelands outside of an abandoned temple, but Lucas gets depressed when Ness is still nowhere to be seen. Along the way, the Pokémon Trainer catches Ivysaur and Charizard. After Charizard is caught, Galleom falls into the ruins, having been knocked down there by Marth, Meta Knight, and Ike. A battle ensues between Lucas, the Pokémon Trainer, and Galleom.
After the battle, Galleom grabs Lucas and the Pokémon Trainer, jumping high into the sky and out of the ruins. Galleom then attempts to detonate a Subspace Bomb as a last-ditch effort. Lucas, finally gaining his courage, uses PK Thunder to sever Galleom's arm, causing the two to plummet to the ground. Just before they hit the bottom, Meta Knight grabs the two and takes them to Marth and Ike. When there, Lucas shakes hands with the Trainer as a sign of their friendship.
Lucas and the other heroes confront the Subspace Gunship, and then journey into subspace to battle Tabuu. He is defeated, but revived by Ness and his companions. He accompanies the heroes into the Great Maze, and can be used to defeat Tabuu at the final battle.
Ness shows up saving Lucas from the giant Pig King Statue, which is soon revealed to be his nemesis, Porky Minch. Both Lucas and Ness team up and defeat Porky and his machine. Afterwards, Wario attacks him with his Dark Cannon, but Ness successfully dodges each shot. Wario, however, then aims at Lucas, forcing Ness to push Lucas out of harm's way and take the trophy-izing arrow from the Dark Cannon. As Lucas is too scared to face Wario, he leaves Ness behind as Wario cackles in the rain. Most of Lucas's story in SSE involves getting revenge on Wario and trying to find Ness.
As Wario is driving his Cargo with Ness' and Peach/Zelda's trophies on board, he finds Luigi's trophy and prepares to take it until he's ambushed by an army of Waddle Dees, who throw Luigi's trophy into the cargo, which is stolen by King Dedede. At his hideout, Dedede puts a badge on Luigi's, Ness's, and Peach/Zelda's trophies before the roof collapses on them and Bowser takes Peach/Zelda's trophy.
Later on, he and Luigi are revived, thanks to the Dedede Badges. Upon inspecting Luigi's badge, he notices that it looks like Dedede, and, assuming that Dedede made them, proceeds to revive him. Upon being revived, King Dedede gives both of them a hug before they team up and rescue most of the other characters to defeat Tabuu.