So that Eve is bitch-slapping you around and you're defenseless? Boohoo. Man it up and deal with it. Here's one way you can:
put yourself up to the task of following The Parasite Eve ultimate weapon formula, also known as the formula for the Most Wrongity-Wrong Parasite Eve weapon EVER. Leave nothing behind with this beast, kill them all! This formula is made/written by my buddy Elliot Rhymeless.

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To begin with, there are two things you'll need in order to make the weapon. The first is somewhere between 2 to 4 Mod Permits or Trading Cards (depending on which gun you choose), and the other is the Super Tool Kit. You could probably make do with the plain Tool Kit or a bunch of Tools and Super Tools, but it'd take a lot more other guns to build the final one that way, and you'd lose all that other stuff if you used regular Tools.

Next, there's the kind of gun I went with to make it. While a lot of experienced PE players will swear by the rifles as the be-all and end-all of starting points for building the best weapon (and rightly so, because of their great range, decent ammo capacity, and respectable power), I've found that once you get rid of the negative add-ons, machine guns are good for more than just their stats, despite having less range than rifles. In my experience Aya's AT gauge seems to refill at different rates depending on what kind of weapon she's got equipped, and that it refills much faster when she's packing a machine gun than a rifle. Anyone who's played PE for any amount of time knows how slowly Aya moves, even while in combat, so it definitely helps for her to have a AT gauge that refills as quickly as possible, and a machine gun can contribute quite a bit to making that happen.

With that in mind, there's about three machine guns that have the best potential for making the weapon, depending on how you play through. If you're going with the normal playthrough of the game, the MP5 PDW (max ability slots: 6, 4 Mod Permits/Trading Cards needed) in the Museum's security monitor room will work... as does the MP5 SD6 (7 slots max, 3 modifications needed) in the Chrysler Bldg., if you want to go through there and get the EX ending.

But if you want the absolute best base weapon for the task, the only way to go is with the P90 (7 slots max, 2 modifications needed)... which you can only get if you go through the real test of patience in PE: collecting 300 pieces of Junk, giving them all to Wayne in the Precinct (through the "Discard Junk" option), and then specifically asking him to make a machine gun. You can get another machine gun if you choose the "leave it to Wayne" option (a PPSh41), but you'll get it at random, and it's actually a little weaker overall than the P90.

After you've gotten one of those guns, gotten rid of the "Random Shot" and the "Rate of Fire" abilities, and maxed out its ability slots, then it's time to add or port over the more-or-less optimum weapon abilities: Command x3 (or x2), Burst, Quickdraw, Critical Bonus, Tranquilizer Rounds, Acid Rounds, and Cyanide Rounds. If you've only got the MP5 PDW, which has just 6 slots to work with, leave out whichever of the three kinds of "Rounds" you don't think you'll need. I'd suggest leaving out the Acid Rounds myself. Trust me, with this gun, the "poison" effect of Acid Rounds is just icing on the cake. ^^

Finally, how to distribute Bonus Points. Since machine guns have pretty much the worst range of all the guns, boosting that is the main priority. It'll take quite a bit to get the gun's range to match that of a rifle (even at the base level), but it can be done. Attack power is the next priority, and then put only as much into Ammo as you think you'll need. If you've got the P90, which has an ammo capacity of 201 rounds right when you get it, you'll never, EVER, have to worry about Aya running out in the middle of a fight. Ever. ^^; The P90's almost like having a second Ammo Crate with you; that's how crazy it is.

And that's it, now you know how to make the absolute most disgustingly powerful weapon in all of PE. I actually took the time to get the P90 and build the gun from that, and not only did having it cut the time it took to beat "pureblood" Eve by half or even more, on one occasion I think I only had to use a single Revive potion before I dropped her. In all honesty, you really don't need a gun this powerful to do anything important in the game... but if you want to make it, that's how you do it. Have fun! ^^