There are many stylistic variations of this kind of thing. Your screenshot is too low-res to discern the exact treatment used for sure. That said:
This takes about 5 minutes and results in a clean, economical construct with a minimum of paths.
Only color is Spot Black.
Two Swatches: Spot Black and 20% tint of Spot Black.
All the offset paths (the inner paths of all the characters) are a single Compound Path and receive a three-stop linear grad fill at 0 degrees.
All the original paths (the outer paths of all the characters) are left separate and a three-stop linear grad fill at 120 degrees is applied (so each outer character has its own grad that can be individually adjusted).
A little individual adjustment of the grads on each outer character can very closely match the arrangement of bevel tones of the original you're trying to emulate. Keep it simple. Study the shading of the emboss edges carefully, and try to see them as linear grads spanning the whole character, not as a bunch of tiny tedious individual details wrapping around the character. Then accomplish the shading with as few grad stops as possible. Understand how to "tighten" or "sharpen" the shifts between grad stops by moving the gamma pointers that are between each pair of adjacent grad stop off-center toward one stop or the other. The tighter the transitions--especially on the bevel facets--the more "sparkle."
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Thanks I'll work on this a bit tonight yet. I appreciate it.
Thank you for the tips everyone. I thought about doing this in photoshop originally, but I did not take courses in the class nor do I have my classroom in a book for reference...so I am not overly familiar with Photoshop. While there are similarities, there are enough differences to make the program feel a bit foreign.
With the tips, I was able to recreate the logo relatively accurately (and faster than I thought). Thanks again.