I think "cognitive gain" is fine here.
I am assuming that it is a philosophical text, so "cognitive", "cognition" and/or "cognitio" are all bound to make an appearance when talking about "Erkenntnis".
I also think "gain in insight" from #1 is fine here. "Erkenntnis" will often be translated as "insight" in these types of texts.
More often though (IMO) "Erkenntnis" will be translated as "knowledge" in texts with this subject matter ("Erkenntnis" and "Wissen" often being more or less synonymous in some contexts).
Other possible alternatives might be:
gain in knowledge / knowledge gain
aquisition of knowledge / knowledge acquistion
("Wissen erlangen" = "to acquire knowledge")
And maybe one of these if the "Erkenntnisgewinn" is a gain in terms of quantity and not just in general:
accumulation of knowledge / knowledge accumulation
compilation of knowledge / knowledge compilation
amassment of knowledge / knowledge amassment
Without knowing the context I am guessing the text is talking about a gain in knowledge in a very general sense though.
You might find reading some translations of Kant's texts helpful in finding some translation pointers.
Hope that helps. Corrections and constructive thoughts on this are very welcome.