“c’est à n’y rien comprendre” is the Good one , “c’est à n’y comprendre rien” is Incorrect ,

this is a little Difficult what you are asking , even for me(i am from France) ,

The difference between “personne n’y comprend rien” & “c’est à n’y rien comprendre” :

“personne n’y comprend rien” mean that NOBODY(Person) is able to Understand ,

“c’est à n’y rien comprendre” mean that the SITUATION/THING is not understandable(Not a Person) , but in familiary Language , you can say for example : “C’est à n’y rien comprendre ce gars”(talking of someone , “gars” = guy)

i am not so good in grammar too , i tried to Answer your Question

In your example you have a subject for the verb comprendre so you need to conjugate it personne n’y comprend rien. You could have written in another sentence personne ne comprend rien à cela which is a sort of expanded way to say the same thing. It is not an occurrence of the idiom c’est à n’y rien comprendre, it is only the use of the verb comprendre and the contracted negative form n’y […] rien.

The idiom c’est à n’y rien comprendre uses the infinitive form of the verb comprendre which does not have any subject in that case and means that you cannot understand a context or a situation.

“Être ou ne pas être, telle est la question”

Generally speaking

In French, the negation of infinitive verb is different than for other tenses. The negative form of “tu es” is “tu n’es pas”, not “tu ne pas es”. With infinitive, however, the “ne pas” is collected before the verb: the negative for of “être” is “ne pas être”, not “n’être pas”. Exceptions may apply, but in everyday speech I can’t think of any.

The negative form of “comprendre” is thus “ne pas comprendre” even though, when conjugated, the usual rules apply and the “pas” jumps behind the verb : “Je ne comprends pas”.

The same rules apply if you use “rien”. The correct infinitive form is “ne rien comprendre“, hence “c’est à n’y rien comprendre” ; the correct conjugated form is “il ne comprend rien”, which gives “personne n’y comprend rien”.

Mind “personne” however: “ne connaître personne“ is correct, “ne personne connaître” is not.

In this particular case

I would consider the extract “à n’y rien comprendre” to be idiomatic. The grammatical correctness of “C’est à n’y comprendre rien” could be debated, but in any case it would be really weird.

Usually when we negate verbs that are conjugated, we follow the rule “SNVP” (subject, ne, verb, pas, or in that case rien). N’ouvrez pas! (dont open).
However if we negate the INFITIVE form, the verb is always at the end. Ne pas ouvrir!

N’y comprend rien is correct.
N’y rien comprend is not correct. It should be n’y rien comprenDRE (an infinitive).