I got a shiny archen from the plume fossil. This is what I did:
1. save in front of the fossil lady facing her direction with one of the fossil on hand.
2. Find a gift pokemon shiny seed in time finder with whatever nature you want.
3. restart your game and hit that seed and immediately mash a to give the lady the fossil, when you get the pokemon back check it's nature.
just repeat number 3 a bit and you will get 1 - 4 different natures. The guy in green in the top right area advances the PID rng randomly so there is no definite nature. Do not save to advance the PID either.
I got a mix of 3 natures and looked in RNG reporter after putting the seed in the main window and my 3 natures were on frame 47 48 and 49. My desired frame was 55 I believe.
After I knew my frame I would just load the game, wait about a second to talk to the lady and see if it landed on the shiny frame. After 4 tries of waiting a random amount of seconds I got my shiny frame.
It can take a while because the guy advances the PID on his own so you cannot control it manually. Wait the amount of seconds it takes to advance the difference in frames. in this case the difference would be 55 - 47 = 8 frames; I got it by luck I guess but if you keep trying and waiting a different amount of time each time you're going to eventually get it.