Entry location: Rand's House (Wireless Tower and Mt. Layuda, to unlock)
Unlike in the original Ranger and like in Shadows of Almia, you can "battle" every boss in the game again. However, unlike in SoA, in which all of the bosses except the final boss were found in the Capture Arena and were much stronger than they originally were, when you rematch a boss in Guardian Signs, they have the same "health" and attack strength as when you first captured them.
To unlock the Many Times, Anytime Capture Machine (which allows you to rematch all bosses and other Pokémon not found in the wild), you must first complete the main story by beating Mewtwo. You must also beat the after-story by beating Articuno, Zapdos, and Moltres. Once you have done these, talk to Nema at Rand's House. She'll tell you that she has made something but needs a lot of electricity to power it. Accept her quest, and capture the following 5 Pokémon (in any order):
1. Jolteon (found at the very top of the Wireless Tower)
2. Ampharos (found in the later dungeons, such as Mt. Layuda and the Sky Fortress)
3. Electrode (found in the western (2nd) cavern of the second floor of Mt. Layuda)
4. Electivire (found in its own room at the top of the eastern (1st) cavern on the second floor of Mt. Layuda)
5. Manetric (found in both caverns on floor 2 of Mt. Layuda)
Once you have all 5 of these Pokémon following you, return to Nema, and she'll take you into her lab. She'll then immediately start up the Many Times, Anytime Capture Machine, and you'll be in an island are that looks identical to Dolce Island (but isn't, for reasons that are obvious if you've played through the story). Here, you'll find every boss and every Pokémon you can't find in the wild, which you can capture again to improve your capture grade and for Experience Points (or to hear their music again, which I like to do). You can't take them with you. You can battle each one as many times as you like, even without leaving. If you lose all your Styler Energy, you won't get a game over. To leave, talk to Nema, who follows you. To get back in, just talk to Nema, who will remain in her lab forever unless you restart your game.
(FINAL NOTES: You can bring all of your Friend Pokémon with you, as well as Ukulele Pichu. Mewtwo is in the last area, but you can only fight its second form again. NOT ALL BOSSES ARE FOUND HERE; Articuno, Zapdos, Moltres, Ho-oh, and Lugia can also be endlessly rematched, but only by going to the respective place where you first battled them and then drawing the respective Ranger Sign.)