The achievement "We Need to go Deeper" can be unlocked by going through an end portal. The description of the achievement reads "Build a portal to the nether." It doesn't make sense that you would unlock "We Need to go Deeper" if you go through an end portal since the description specifically says the Nether. It is possible to go through an end portal without going into the nether at all. This can be done on a server, creative world, or trading eyes of ender through villagers.

What I though would happen
When I stepped through an end portal with the achievement "We Need to go Deeper" not yet taken but the prerequisites unlocked, I would not get the achievement because that is not what the description reads.

What actually happened
When stepping through an end portal, I unlocked "We Need to go Deeper"

Steps:
Wipe you stats
Unlock all prerequisites for "We Need to go Deeper"
Go through an end portal via the possible ways described above