We only have one trailer and a couple of screenshots and magazine scans, but we do have enough information to tell you who we think the enemies are. This section will be a king of beastiary. We have no official names, so they enemies will be named and described as best they can.
Pulse Solider
We know that Pulse is attacking Cocoon, and Lightning has been seen fighting these soliders, so it is safe to assume they are the attacking soliders from Pulse. There seems to be more than one type of solider. Some have guns like the picture to the right, and the one which lightning clashes with in the trailer looks as though he has an electric batton type thing, possibly for stunning prisoners. (See left pic)
Robotic Solider
Lightning does not interact with a robotic solider in the trailer, though one can be seen in the background. It is not clear how they attack or how powerful they are, but i would assume a bit stronger than the average pulse solider.
Attack Dog
Lightning is seen fighting these in the trailer. They run on all four legs and use their large blue claws to cut and hold on to their enemy with their teeth. They seem to be armoured, however it is not clear if it was given to them, or part of them.
Notice: The next two monsters are the same monster at a different angle. The TGS 2006 trailer is proof of this. Thanks to forum member Vikz for pointing this out.
Behemoth look alike monster
This enemy is not shown in the E3 2006 trailer, nor is it shown in any other trailer, so nothing is known about it. It does however look like an enemy common in Final Fantasy - Behemoth. It looks heavily armoured and very dangerous. It seems like a monster that would take a fair amount of skill to take down. Whether it is in fact Behemoth is unknown, but it would be strange to make a monster so similar, unless they have a behemoth monster that looks more like what we're used to.
Dragon Monster with sword
This monster is seen in a quick, stylish battle with lots of flips in, fighting Lightning in the Tokyo Gameshow trailer. It is only shown for a brief amount of time, but from the way it looks suggests, its very powerful. When lightning tries to attack it, it throws her right back.
Flying Robot
This robot is seen in the E3 2006 trailer. It faces off against Lightning right at the end of the trailer, we are yet to see it in action. However, it peruses the train which lightning is on, so we assume that it is targeted for her. It has large Buzz-saw like saws for claws probably for cutting through metal to get to its target, then mincing them for a quick death.