The very first acts of Guardians was to banish nearly all magic from universe into starheart. Originally told in GL v2 111 and recounted in GL Corps Quarterly 7. In GL v2 112 its stated to be able to scatter through Omniverse.
Guardians battle and stalemate Nekron, stop galaxies from destruction, defeat Krona after Nekron is distracted by Hal, seal the rift between universes and return the whole universe to its original state when it was near destruction. Beastly feats.
When Sinestro takes over the power of CPB (powerful enough to destroy the universe by creating a black hole) and Hal Jordan failed to defeat him by his own power, a guardian gives him a portion of his power to defeat Sinestro.
Turned out they are controlled by the Controller who takes on entire GL corps and Darkstars simultaneously and kicks all of their asses. He is only beaten when his control fails and the Triarch turns upon him and later turn the entire planet into paradise.
When John Stewart is given the power of a Guardian, he resurrects Katma Tui, defeats several GLs including Hal, Guy, Kilowog and JLA (J'onn, Power Girl and Flash) and a world destroying alien armada together, shows omniscience (Knows what's happening on Earth from Oa) and omnipresence etc.
Child Guardians and Ganthet stop a barrage of quantum singularities, each one capable of destroying entire suns (and specified as objects of infinite gravity). Absorbing just one such singularity nearly killed Kyle.
Xadai (Kilowog's demons in afterlife) surprise Ganthet and overpowered him. Later Ganthet rips open the realm of afterlife and after an amped Kyle and Kilowog as Dark Lantern (Someone powerful enough to stomp Justice League, Sentinel and even cut Zero Hour Parallax in half) struggle with Xadai, Ganthet beats them with a literal clap of his hands.
Now comes a Guardian's most famous showing. Krona from JLA/Avengers.
First, Origin of Krona. Its mistaken that he was powered up before he was destroying universes but that's not shown anywhere. He is your average Maltusian before Guardians evolved into what they were today.
Hal had absorbed chronal energies left after COIE to destroy time stream. Here he destroys an entire universe by opening an entropy rift. Later Extant says there are other entropy rifts he was not responsible for.