Note: If your class isn't very good at soloing, you might need good gear.
Step 1: Head on over to the Throne of the Tides in Vash'jir's Shimmering Expanse
Step 2: Clear all the necessary trash leading up to the first boss. (Lady Naz'jar)
Step 2.5: Kill the first boss and use the control panel located at the entrance into Naz'jar's room.
Step 3: Using the teleporter, teleport back to the start of the instance and turn to the left corridor, leading to the Neptulon encounter.
Step 4: Kill the 2 (or 3?) Tainted Sentry patrolling the corridor (make sure you leave the 2 guarding the door to the final encounter alive).
Step 5: Keep killing the Unstable Corruptions (3095 HP)
I spent 55 minutes in there and procured 844 charms. I can therefore quite assuredly say this is the fastest way to get Lovely Charms at this time.