The items themselves are tied to the 5 different biomes, and each biome has two Archaeological items each; one tied to Fishing Traps and one tied to Digging.
The digging related Archaeological items has a small chance to drop any time you use your Shovel to dig in the ground. Like any rare item, the chance of getting it will be increased by things that increase your chance to find rare items, like Liquid Luck, Accessories and a better Shovel. Dig spots can also have a higher chance to drop rare items, so make sure to dig these.
If you don't have a Shovel yet, pick up the "Farming" skill to unlock it, and remember to upgrade it as high as you can, since higher upgraded Shovels will drop better loot and give a wider dig radius.
|There's a dig spot a few bloks ahead of the character, so look for these and dig them!|
Like with the digging, things such as increased rare items found will also affect the Fish Traps. These also counts as buildings, so feel free to use any items or other buildings that improve the output from buildings, since this will make the Fish Traps better. Some things to use are Builder's Scroll and Liquid Luck.
I would also suggest getting a Droid to do all the harvesting for you, since the Droid will automatically collect any full Fish Trap. This means that you can just go AFK close to a few Fish Traps, and the Droid will loot them as soon as they are ready. Set up a bunch of Fish Traps and take a ten minute break, and you will likely have the Archaeological item you need when you return.
Full list of all Archaeological itemsAnchor: Found by using Fish Trap in the Grass Biome.
Fossil: Found by digging in the Grass Biome.
Dino Egg: Found by digging in the Fire Biome.
Lava Eel: Found by using Fish Traps in the Fire Biome.
Frozen Relic: Found by digging in the Winter Biome.
Frozen Squid: Found by using a Fish Trap in the Winter biome.
Kapala: Found by digging in the Graveyard biome.
Skeleton Fish: Found by using Fish Traps in the Graveyard Biome.
Sphynx: Found by digging in the Desert Biome.
Sunken Ankh: Found by using Fish Traps in the Desert Biome.
Get the Archaeological items with the Slot Machine
Once you unlock the Slot Machine, you will have an alternative method to unlocking the Archaeological items, because they all have a small chance to be obtained by winning the slots. So try this out if you won't want to bother with digging or setting up Fishing Traps.