Eragon has the Eldunarí and Saphira mentally backing him. Most of the Eldunarí are so well versed in mental magic that they were able to control certain events in the world. All of the thousands of Eldunarí, Saphira, and Eragon can join their mental assault, target Link specifically, destroy his mental defenses and drive him insane.
Again, they'd need a showing that puts them above Fi.
Now imagine thousands of sentient beings attacking, each with the same mental force as ONE of the objects Link was able to resist, all attacking at once, they would easily break his mental defenses and could even kill Link from there. Eragon may not even have to draw Brisingr.
You seem to be missing the scale of what Fi has overcome.
She's matched the power of the completed triforce itself, something which is said to be omnipotent, but again, statements like that can't be taken as truth. The triforce does have more claim to this than Eragon does, however, if his claim to it is indeed what's been shared with me in this thread.
Eragon's power comes from dragon souls, he has many, but a limited number. There is, somewhere, a definite end to his power. The same is true of the Triforce, which is said to be omnipotent, has shown to be above silly things like time and space during the split occuring in OoT, created an entire alternate world with its own sun and sky to mirror the real world, in an alternate dimension which radiated so much evil power across that dimension that it had to be sealed by the six sages to prevent disaster, and even through the seal it's power could be felt, manipulating the world, mind controlling the entire Hylian army and king, causing earthquakes and natural disasters and creating incredibly dangerous monsters.
The triforce is hardcore, but not omnipotent. Nor is Eragon's power truly 'endless'. Fi's ability to dispel, repel, reflect, and otherwise just tell magic to piss off is on a scale where it cannot be said conclusively that Eragon can bypass her.
The mirror of twilight and fused shadows are just demonstrations that her protection from magic also applies to mind effecting powers. They are not the full extent of her power.
Beyond this, Link carries the Triforce of courage as well, which also has some degree of protection.
Essentially, Link has the exact kind of defense required to best Eragon, it's odd you made such a perfectly lined up thread, honestly.
Still, it cannot be said who is greater between Fi and Eragon. And in any situation where Fi is greater, Link wins.
If Fi can be overcome, Link will still pull wins due to acting first due to how much more physically imposing his non-magical attacks are.
Edit: And drawing Brisingir would be tantamount to suicide. Eragon cannot physically engage Link. mmm