If the 1st player escapes Nyogtha's attempt to pull him underground, then what happens during the Epic Battle? Is Nyotha's combat rating -3 only for this turn for the 1st player or is it -3 for the rest of the game? If the benefit is only for the current turn, then it will be useless if the Investigator's attack 1st (which is what usually occurs during Epic Battle.) If the 1st player survives the 1st attack by Nyogtha, then will this AO try again on every subsequent turn that there are survivors left to be devoured?

On any given turn, only one investigator gets to take advantage of the -3: the First Player.

Unfortunately, this also means that that player has a chance of being killed outright.

Tibs said:

Yes I think you are.

Nyogtha's tentacle appears before the 1st player.

His tentacle is his weak point, and the investigator attacks it.

Nyogtha attempts to drag the 1st player down. Whether or not the investigator dies, the investigator still got in his attack.

Thematic reasons for the -3 modifier, Nice!

This is is a nitpick, but: the thematic explanation is actually that Nyogtha is largely undergound. The first player is always pulled underground at the start of the round (or, well, after Upkeep); this means that the investigator has a good chance of being eaten, but it also means that he is able to attack Nyogtha directly, whereas the others aboveground can only attack its tendrils. This why Nyogtha's The Creature Surfaces card, which (surprisingly enough) entails Nyogtha surfacing, gives everyone the bonus to attack.