While I think Alduin is very strong, I believe there is no way Alduin will be able to defeat Eldrad Ulthran.

I am just going to point out some reasons I think why, but this is just my opinion, not a fact.

1. Alduin was killed by the Dragonborn (With the help of 3 other nords who were able to shout as well.) He was slain by Elder Scroll tier weapons.

2. Eldrad Ulthran is the second strongest Psyker in the entire galaxy (excluding Magnus the Red and Tzeentch since they have natural advantages.)

3. If I look it from this way, Eldrad was able to defeat Abaddon the Despoiler in combat, the very same person who managed to kill a cloned Horus and has the blessing of all 4 chaos gods. It's one heck of an accomplishment for someone to beat Abaddon like that, especially considering what Abaddon what wargear Abaddon has.

4. While Alduin can fly in the air, he is pretty much in the disadvantage when it comes to speed, he is a dragon and will have trouble keeping up with Eldrad. (Eldar are insanely fast overall.)

5. Alduin has perhaps one advantage tough, Thums (shouts.) But it depends on what kind of Shouts he would use, and we also have to keep in mind that Eldrad as a Psyker draws his powers from the Warp itself, wich means he could do some really dangerous things back (Eldrad's armour is something I am not sure about tough, while it has a protection ward, I can't really confirm if it would protect against Alduin's shouts, tough it will protect well against physical attacks and breath attacks.

6. Eldrad is a farseer, wich means he can see in the future (That is one of the unique abilities of Eldar Farseers.) And considering Eldrad's mastery of his physic powers, it is almost impossible to imagine how far he could see.