Batman and Wolverine win this. Luckily Batman has protocols in place for such an event.
Here's how it goes down.
As the five cosmic entities approach Earth, alarms go off in the Batcave. Batman realizing that he is outmatched for the first time in his life, sets into motion the dreaded Wolverine Gambit.
Using a JLA transporter keyed to allow travel between the DC and Marvel Universes, Batman transports Wolverine to the DC Universe.
Batman: You know why you're here?
Wolverine: I'm not stupid, bub. Let's do this.
Lucifer, Michael, the Living Tribunal, Phoenix, and the Spectre materialize within the Batcave.
The Living Tribunal and Spectre speaking as one: For repeated violations of the Law of Reasonable Suspension of Disbelief, The One Above All! (The Presence!) has ordered your removal from Continuity.
Lucifer (to Michael): Let's go.
Michael: God has ordered ...
Lucifer cutting Michael off: Look behind the giant penny.
Michael: Ah ...
Lucifer and Michael disappear from sight as Superman steps out from behind the penny.
The Living Tribunal, Spectre, and Phoenix: No!! No!!!! No!!!!!!
Spectre: I've faithfully served the Presence!
Phoenix: What have I done to deserve this?
The Living Tribunal: I accept my fate.
With speed defying defying description, Superman lands haymaker after haymaker on the Spectre until the impossible happens and the Spectre falls!
Wolverine (to the Living Tribunal): I've been waiting a long time for this, bub!
Wolverine kicks the Living Tribunal in the crotch and lays him out with his best Lobo-busting punch.
The Phoenix confused by the carnage unleashed around her makes a fateful mistake and looks into Batman's eyes. Staggered by his fearsome presence and steely resolve, she stumbles backwards as Batman takes her out with a Bat-kick (TM).
Epilogue:
Wolverine (to Batman): What's the deal with the Big Blue Boy Scout? I thought our jobber auras could defeat anyone.
Batman: Against five of the most powerful entities in all comics? I figured our only chance would be in a Superman/Batman comic.
Superman: Glad to help!