The Big Finish
When he is first mentioned, Mon-El and Superboy are pursuing him through time after he has a fight with Cosmic Boy and Sun Boy, but we never saw this initial encounter and it's never recapped in detail. All we get is an ongoing subplot where the Legion are unable to break past the "iron curtain of time" 30 days in the future.
Whether this is a set point thirty days from the initial encounter, or a moving point that is always thirty days from the current time is unclear. I originally assumed it was a fixed point and the Legion were facing a countdown to a major battle, but their adventures continue on for issue after issue without it appearing to get any closer, or their being especially concerned about an approaching deadline.
The penultimate story in the collection features Superboy's evil babysitter, Dev-Em. This appears to be a sequel to a Superboy solo story but unusually there's no editor note to tell you. The short version is Dev-Em was bad; now he's good but he's pretending to be bad. And the Science Police, who you will remember claim there is no crime worth bothering about and the best way to deal with a planetary threat is to send in a bunch of teenagers rather than try diplomacy or military action, are now found to have a counter intelligence corps. Or maybe the Interstellar Counter Intelligence Corps has taken over the Science Police in a bloodless and entirely uneventful coup, since the Legion initially say that's who they will turn Dev-Em over to when they believe he is a criminal.
Either way, it's obviously the same lot because they decide that rather than send Dev-Em to complete the mission they've trained him for, they'd prefer to send Superboy in a plastic mask pretending to be Dev-Em. At least if they'd sent Mon-El they wouldn't have needed the contrived deus ex machina to get our hero out of the trap when the villain pulls out the kryptonite.
And so we come to the final entry, and the first actual appearance (of the back of the head) of the Time Trapper. It transpires that the Legion have a Secret Weapon. A weapon so dangerous and powerful that they don't want anyone to know about it. Except somehow the Time Trapper has heard of it and cons the Legion into letting him torture them to get the secret out of them.
Under the guise of some Commander Wilson of the Science Police, who are back in charge of running the universe by ignoring most of the crime going on, he persuades the legionnaires to go through a simulated interrogation to see if any of them will crack and give out the secret.
Problems with this: first, they know it's not real so why do they get so scared? Second, I'm not sure what the secret is they are supposed to be hiding since the weapon is quite a complex piece of equipment that they need to build from scratch. It's not like they are giving away a location for this doomsday device. They'd need to draw diagrams.
Anyway, we get a series of scenes of legionnaires being put through tests and either overcoming them or failing in a way that prevents the secret being given, like Shrinking Violet getting so small that her voice can't be heard, because a thousand years in the future they don't have the technology to pick up faint sounds. And Lightning Lad fails and gets locked up in a giant hamster ball forever, except no, it was a trick. He spotted that the commander was a fake and gave him the wrong information. Was it too much to ask that he tell his friends instead so they could prevent the villain's escape?
So the Time Trapper proves that he doesn't actually need any more doomsday devices as he is already powerful enough to throw suns around, and the Legion run up their ultimate weapon out of household objects they find lying around, and siphon off all the power of the entire universe to blow up the errant suns.
Seems like overkill to me. I mean suns are big to you and me, but on a universal scale they are barely dust. Of course the Legion live in a very small universe, as has been noted earlier, so things may be different for them.
And so all is well and we end on a totally sitcom note as newly thin and no longer Bouncing boy introduces his girlfriend who is a little chubby, and our heroes are surprised because of course now he is thin he doesn't need to date fat chicks. Was that even funny in 1964?