It's pretty simple. I no longer have the full Adobe suite, but I can show you the same basic steps as a Photoshop action.
Open any EPS in Illustrator. It doesn't matter which one. Click on the Actions palette and then either an existing folder, or create a new folder for your personal actions. Here, I selected an old folder of my own stuff.
Select the folder in the Actions palette you want to have your item under (as I did with the JKL Studios folder), then click the square boxed + button to start a new action. Something similar to this will appear.
Give it any name that makes sense to you, then click the Record button.
The only thing you need to record is a Save function. Important: choose Save As, not just Save from the menu and then select either an .ai file or PDF from the save palette menu. Here, I used the closest thing I could choose in Photoshop.
If you choose PDF, it will ask for some settings. Acrobat 5 is the default compatibility, though you should probably use a higher version to make sure it doesn't drop out image features that version 5 can't save. Make sure to use [High Quality Print].
Be sure to use Do Not Downsample so any embedded raster images are not altered from their native resolution.
Click Save PDF (or however Illustrator has it marked).
During all of this, the red record button will be active on the Actions palette. Click the stop button to the left of it to finish the recording.
Now, gather all of your EPS images into one folder. Create a new empty folder as a location to save the converted items to.
Again, this is Photoshop, but the menu choice should be nearly identical in Illustrator. File > Automate > Batch.
Usually, the last folder and action you were working with will automatically be chosen at the upper left (image below). Change it to point to your new action as necessary. Click the Choose button under Source > Folder and select the folder all of the EPS images are in. Click the Choose button to the right and select the empty folder for the converted images. Make sure the check box for Override Action "Save As" Commands is on, or it will try to save all of the images to wherever you saved the file when creating the action.
Click OK and sit back while Illustrator chugs through all of your EPS files on its own.
If it stops before finishing, that will almost always be because there's a profile mismatch. So, before starting the automated conversions, check AI's color settings. Have it set to convert to your working RGB (I presume these are all RGB files), and make sure the Ask When Opening check boxes are off for both Profile Mismatches and Missing Profiles. Then the conversions will either convert or assign as necessary without stopping.
