I've always seen Archived Memories almost like a Double that says "Copy an operation in Archives" - often one you've just played out of HQ as your first click. The ability to effectively mirror any operation in HQ or Archives makes it pretty powerful when played at the right time.
Archived Memories works particularly well with operations that benefit from being played twice in a single turn to achieve a quick tempo swing or damage boost, especially if they're the conditional "play only if X" type.
With that in mind, here are a few operations that go nicely with it:
Bad Times (Trash 4MU's worth of programs for 8 credits? Yespls)
Midseason Replacements (After they've spent everything fighting off the first one)
Power Grid Overload (As above)