Hardcore Expeditions are instanced Dungeons. For these Dungeons you need special maps to enter them.
They have increased difficulty and fame per level.

The HCE maps look like stars with a number. The number indicates the level of the map.
There are different typ of maps:
The level of each map indicates the general difficulty of the map.
You can compare a level 1 map with a T6-T7 open world dungeon.
With each level the following stats will increas:
Percentages are from the official wiki and might not be up to date.
To do a Map you will need the following:
The map can be bought at the market or found in various chests all around the world.
out of our experience the following IP limits make your life easier:
These IP limits are our experience and can be lower or higher depending on how well the team knows each other, specs and level of gear.
You have to be in one party and all near the same portal. Otherwise the signing up won't work.
Bring lots of food! In case you get downed and killed by the mobs in a HCE map, you will loose your food buff! So bring a full stack with you.
You can leave your mount behind. It will only get damaged and increases your repair costs.
Go to any expedition master in the world

Then click on him and go to the last tab

here you can insert your map and get additional
Once you have chosen a map, the party leader clicks on register.
Then all must register and wait for the map to load.
After a short time, everyone needs to click start

By clicking it, you channel the entrance. Onc all fully channeled you are teleported to a new location.
Once you loaded into the expedition you will notice a timer on the right side of your screen.

This timer indicates two things:
This is the time you have to finish the map without getting kicked out.
You have to beat the map and fulfill all conditions above the timer to level up the map.
If you can do it, your map will switch randomly to another map and one level higher.