WARNING: The following contains spoilers for Dark Nights: Death Metal Guidebook by Joshua Williamson, Scott Snyder, James Tynion IV, Doug Mahnke, Jaime Mendoza, David Baron and Tom Napolitano, on sale now.
After the events of Dark Nights: Metal, by Scott Snyder and Greg Capullo, Perpetua was released from the Source Wall. Snyder picks up this story in his 39-issue Justice League run. Here, Snyder details how Perpetua continues to get stronger as she gathers her forces to invade and take over the Multiverse. By Scott Snyder, Jorge Jimenez and Daniel Sampere's Justice League #39, the battle is lost.
Dark Nights: Death Metal Guidebook provides more background and details about how Perpetua defeated the Justice League and successfully took over the Multiverse.
In the finale of the "Justice/Doom War" story in Justice League #39, Perpetua obliterates the Justice League in their final confrontation. Before they are wiped out of existence, the Quintessence saves the Justice League by snatching them out of reality. The Quintessence is a group of all-powerful beings who keep a check on the order of the universe. The group members consult each other and consider themselves the guardians of eternity. This cabal first appeared in 1996, in Kingdom Come #3, by Mark Waid and Alex Ross.
The members of the Quintessence in Justice League #39 are Ganthet, Phantom Stranger, Hera, Shazam, Highfather and the Spectre. When they grabbed the Leaguers before Perpetua killed them, the Quintessence imbued them with the connective energy of the Multiverse in order to fight Perpetua. Connective energy is the cumulative positive energy in the Multiverse. It is the energy that comes from the Speed Force, the emotional spectrum and the "forces of justice" itself.
Perpetua harnesses Crisis energy, which is made up of things like Anti-Life, chaos magic and the forces of doom. Crisis energy is the negative energy in opposition to connective energy. In the pages of Snyder and Capullo's Dark Nights: Death Metal #1, Dr. Manhattan, who is full of connective energy, attempted to mend the damage done by previous crises, but he failed. This is why the Quintessence intervened. They gave the connective energy to the Leaguers in order to level the playing field a little more against Perpetua.
Between Justice League #39 and Death Metal #1, there was another huge battle that exhausted both energies "in a blast so powerful it burned out the sun." The details of this battle are still unknown, but it is clear Wonder Woman was at the center of it. Wonder Woman faced off against Perpetua and ultimately failed. When the other Leaguers pressed Wonder Woman to tell them what happened in that battle, all she remembered was she was the last hero to fall and "fear... fear and then a blast of energy."
When the defeated Justice League returned to earth, they came home to a world overrun by The Batman Who Laughs and his army of evil Batmen, the Dark Knights. Trying to play catchup, the League divided into groups and tried to take on the dark forces individually. This led to the Justice League losing Earth.
Given a second chance by the Quintessence, the Justice League still couldn't take down Perpetua. The key seems to lie with Wonder Woman and her battle with the Mother of the Multiverse. Lex Luthor hints that victory may rest on whether Wonder Woman remembers what "has been forgotten." It's unclear whether Wonder Woman still holds the connective energy to take down Perpetua.