This is quite easy actually. It might take a try or two but here's what I do.
While alone means being the only person in the game instance, easiest would be picking solo.
Bring Oxylus if you got one, if not, any sentinel. If not, empty.
Make sure to unequip your sentinel mods that attack or effect enemy.
Get Ivara or Loki, built for maximum duration/efficiency.
Go to Plains of Eidolon with solo mode selected.
Go to any fishing location close to Geyser Pond.
After you catch a fish, immediately jump to your archwing and go to Geyser Pond. Be careful not to kill enemies before you catch a fish so they will be there. You can get one immediately as you land with slam attack, or as fast as you can kill one.
Cave entrance next to Geyser Pond has a lot of gems. Mine one and you're done. This should take around 20 seconds, might be couple of tries if you're not fast enough.
