Eureka is an instanced area made up of four islands with a maximum of 144 players per instance. You will have a series of quests to complete which will unlock based on your elemental level. You will gradually gain access to relic weapons and armor from Stormblood which will be useful for you to complete the dungeon on the last island with other players.
Quest: And We Shall Call It Eureka
To have all the list of actions, the combinations to do to get them, trackers for eureka or even a guide for BA, you can use : https://ffxiv-eureka.com
If you want to forecast a farm day with specific weather, you can use the weather tool.
If you want to know the full list of FATES and their reward for each island in Eureka : Fates.
For the majority of your levels, the best is to complete the fates, and complete your Challenge Log.
Also use Potion of Harmony to increase experience gained.
Look for fates trains to follow the players who will make them appear, do not hesitate to communicate by shouting.
Outside of fates, if you meet players and want to group up with them, be careful not to have too big of a level difference between you, otherwise you might not gain experience when killing monsters.
One trick to gaining experience quickly is to use a mirror logo with Sprites.
Remove your equipment, move away from the Sprites to put a first mirror, once activated, get closer, refresh the mirror regularly to aggro the Sprites, they kill themselves with their attack which will be reflected.
You will not gain xp on Sprites if your level difference is too great.
To make a mirror you will need :
Talk to Krile, then to Gerolt. Unlocks use of Gerolt for Eureka weapon and armor enhancement, and Expedition Lockpick.
Talk to Krile. Proceed inside the Early Natural History Society Observatory (x13.5, y20.2) and interact with the Confluence. Return and talk to Krile.
Talk to Krile. Proceed to the The Orchard (x24.4, y23.1) below the cliff and interact with the Confluence. Return and talk to Krile.
You can now attune to the Abandoned Laboratory and Windtorn Cabin Aetherytes.
Talk to Krile. Proceed to the The Val River Swale (x20.9, y13.0) near the waterfall and interact with the Confluence. Return and talk to Krile.
Talk to Krile. Proceed to the Uncanny Valley (x32.8, y18.3) and interact with the Confluence. Return and talk to Krile. Proceed to the Aethernet Control (x25.5, y16.1) and interact with the Aethernet Relay. Interact with the Aethernet Relay again and trade 99 Anemos Crystals. Return and talk to Krile.
Talk to Krile.
Talk to Krile. Locate the Depleted Aetherial Stream at The Cones (x16.5, y28.8) (upper level on a raised grassy hill). Return and talk to Krile.
You can attune to the aetheryte at Vlondette's Retreat.
Talk to Krile. Locate the Depleted Aetherial Stream at The Val River Belly (x26.7, y30.7). Return and talk to Krile.
You can attune to the aetheryte at Geothermal Studies.
Talk to Krile. Next, locate the magicite at The Eastern Edge (x30.9, y20.7), and also inspect The Eastern Edge (x30.7, y21.0) and return to Krile. You can also speak with Gerolt any time after first speaking to Krile to unlock Eureka Pagos weapon enhancement.
You can attune to the aetheryte at Gravitational Studies.
Talk to Krile. Talk to Ejika Tsunjika on a ledge in The Western Edge. You will need to walk through Hot Water and drop down at x9.9, y21.3. Return and talk to Krile.
Talk to Krile. Locate the aether column at The Fumarole (x21.8, y12.4). Return and talk to Krile.
Talk to Krile and then talk to Krile again in The Living Foundry just to the north. Then return to the center of Northpoint and talk to Gerolt and then Drake. Use the Logos Manipulator to unlock it, select the Paralyze L logogram and extract the mneme. Talk again to Drake. Talk to Krile. Travel to x27.7, y27.1 in Northeastern Ice Needles and interact with the confluence, then return and talk one last time to Krile.
You can attune to the aetheryte at The Dragon Star Observatory.
Talk to Krile and then Drake. Head to The Surgate Town House and interact with the "Promising Scrap" at x18.6, y30.6. Return and talk to Drake and unlock additional capacity with the logos manipulator.
Talk to Krile. Head to The Firing Chamber (x23.8, y17) and interact with the confluence. Talk to Krile to complete the quest.
You can attune to the aetheryte at The Firing Chamber.
Talk to Krile and head over to West Flamerock (x17.2, y11.6) and pick up the confluence. Once you have done so, return to Krile to complete the quest.
You can attune to the aetheryte at Carbonatite Quarry.
Talk to Krile and after a few cutscenes, speak with her again at The Living Foundry.
Talk to Krile and then proceed to pick up the confluence at East Flamerock (x34.0, y7.3). Return to Krile and speak with her before travelling south to The Cavern of the Second Cant (x14.5, y37.6).
Talk to Krile and then, after a cutscene, to Gerolt. After another cutscene, speak again with Krile. Upon finishing the quest, you can speak with Gerolt again to begin purchasing the Hydatos weapons; you must have a matching, finished Pyros weapon to do so.
Talk to Krile. Head to The Central Columns (x20.3, y24.8) and talk again to Krile. Head south to The Val River Source (x25.7, y30.7) to find the Pooled Aether. Return to the The Central Columns and speak to Krile.
You can attune to the aetheryte at Unverified Research.
Talk to Krile. Head to The Western Columns (x10.6, y29.6) and talk to Krile again. Head to The West Val River Bank (x6.5, y15.7) to find the Pooled Aether after walking up the large column. Return to The Western Columns (x10.6, y29.6) and talk to Krile.
You can attune to the aetheryte at Dormitory.
Talk to Krile at the The Western Columns (x10.6, y29.6). Then head east to The Eastern Columns (x31.3, y27.2) and talk to Krile again. Head north to The East Val River Bank (x30.8, y14.4) to find the Pooled Aether. Return to The Eastern Columns (x31.3, y27.2) and talk to Krile.
Talk to Krile at the The Eastern Columns (x31.3, y27.2). Head to The Aetherbridge Foundation (x24.0, y30.6) and talk again to Krile. Head into the Headquarters Entrance and talk to Krile, then talk to her again in the Board Room. Interact with the Scattered Tomes and talk again to Krile for a few lengthy cutscenes. Choose between Krile's path (sealing) or that of Ejika Tsunjika (destruction) for another cutscene. Return to Central Point and talk to Ejika Tsunjika (when doing Krile's path) or Krile (when doing Ejika's path) to complete the quest.
Able to use the Aetherial Nodes to access The Baldesion Arsenal. Speak with the Expedition Scholar to unlock.
In order to farm Cold-warped Lockboxes, you have to find monsters, which level is higher than yours and which will mutate under the given weather and time. It is advised to have a group of multiple people in order to tackle higher levelled mobs than you could do alone.
Common mobs used for lockbox farms are :
In general try the highest level mob possible, but check for the specific time and weather conditions.
Allows you to obtain the following rewards :
In order to farm Heat-warped Lockboxes, you have to find monsters, which level is higher than yours and which will mutate under the given weather and time. It is advised to have a group of multiple people in order to tackle higher levelled mobs than you could do alone.
Common mobs used for lockbox farms are :
In general try the highest level mob possible, but check for the specific time and weather conditions.
Allows you to obtain the following rewards :
In order to farm Moisture-warped Lockbox, you have to find monsters, which level is higher than yours and which will mutate under the given weather and time. It is advised to have a group of multiple people in order to tackle higher levelled mobs than you could do alone.
Common mobs used for lockbox farms are :
In general try the highest level mob possible, but check for the specific time and weather conditions.
Allows you to obtain the following rewards :
Do not hesitate to use the site weather tool to find out what time to do your farms : Eorzea Weather
If you want to see all of the monsters and their mutation : Eureka Bestiary (EN)