I would just shoot them with bullets. And then more bullets. And then have a bullet party on their metal corpses.
More Dakka solves everything.
So, while we're still waiting for this to start, why don't we do a bit of world-building?
Magic, obviously, exists in this setting (most of the mechs seemed to be powered by mana reactors), but to what degree? I imagine it's probably at least somewhat rare (with Gensokyo likely serving as an exception to this), making naturally-talented magicians valuable mecha pilots.
Also, what relation do the different nations/states/factions have with each other, and where are they located, if it's not already been stated? In Blaz Blue, the NOL is essentially the only world power; in a crossover setting it seems more fitting that they're in charge of most of Western Europe, which would probably fit nicely with the other main factions being the U Fo MD in the USA and Gensokyo in Japan. As for relations, I can imagine the NOL, what with it's SCP Foundation-like obsession with controlling dangerous magical artifacts, would be just short of at war with Gensokyo and its Fantasy Kitchen Sink nature.
Thoughts?
In canon Neo Arcadia's the "last bastion of humanity" and has operations all over the world (they have a naval base I believe in the Antarctic). I'm... not sure how to translate that into their role here. They have access to extremely advanced technology... which, unfortunately, they appear to pour into their military more than anything else (though NA itself has a little bit of Crystal Spires and Togas going on, especially at the Neo Arcadia Shrine and Area X-2, which extends into space). Use of automation is widespread, and there are lots of humanoid robots (reploids). I have no clue how their economy operates, though presumably they sell high tech goods in return for energy (since they're apparently in the middle of an energy crisis... even though it only gets lip service in the games).
Despite there being a council of sorts, NA appears to be usually ruled by a single person (X prior to the Zero series, Copy X during the first two games and part of the third, and Dr. Weil during the last bit of the third and the whole of the fourth game). Since Hidden Phantom hasn't tried to blow himself up in order to destroy Zero, presumably this means Copy X is in charge (unless he was rebuilt, in which case we could be dealing with Copy X Mk II or Dr. Weil. I doubt this since it'd be non-canon).
X is considered an almost godlike figure by most Neo Arcadians, despite the fact that NA is a rather repressive regime.
I imagine that Neo Arcadia's relations with the rest of the world would be similar to those between the USSR and the West: chilly with the occasional bout of gunboat diplomacy and flexing of military muscles from NA. I still have no clue where they'd be situated, though.
Locking you up on radar since '09NA's mechs are probably powered by an upscaled version of the fusion reactors used by reploids.
Also, just because NA really loves their mythological references, their mechs use the JOTUN piloting system*.
And speaking of beings using their own powers to power things, Mino Magnus uses his immense electromagnetic capabilities to power a giant mass driver... which is usually used to transport things. Much like Utsuho, he's not terribly bright.
Locking you up on radar since '09Borderlands is a used future, but Lilith, being a mercenary, can pretty much be from anywhere.
Actually, considering the similarity (if rather large power disparity) between Lilith's phasewalker abilities and Mu-13's godlike skills, maybe make the scientist who studied her be behind that project, synthesising and weaponising those abilities.
So...uh...how do we start? Where do we start? We kinda need an event to get all our attentions and make us work together.
Hmm...
The Glorft get lost and wind up on the wrong planet?
They'd be prefect mooks for us to demolish as we get to know each other.

The word 'submersible' comes to mind, and considering that most of our entries have focused on ground or aerial combat, it could make for some creative combat scenes...