My friend is embarrassed about exposing his body when going to the mikvah for nocturnal emission. How should I comfort him as a friend and tell it's importance? Is there any solution for his problem?
Find a distant Mikveh where nobody knows him and different hours
Find a real frum Mikveh - Haredi guys don't care at all
re-Consider the importance of going to Mikveh - it's not a necessity, not a Mitzvah, he might want to suspend this practice until he works those psychological problems out.
Some say pouring enough water in the shower can suffice.
Consult a serious Rabbi.
How should I comfort him as a friend and tell it's importance?
It's not important.
Is there any solution for his problem?
He doesn't have to go to the Mikveh after a nocturnal emission.
Men have no obligation to go to Mikve after nocturnal emissions.
Ezra the Scribe instituted this concept and it has subsequently been abandoned, as is clearly documented in Shulchan Aruch, Orach Chaim, Siman 88, which is titled A Ba'al Keri is premitted to say Shema:
בעל קרי מותר בק"ש. ובו ס"א:
כל הטמאים קורין בתורה וקורין ק"ש ומתפללין חוץ מבעל קרי שהוציאו עזרא מכלל הטמאים ואסרו בין בד"ת בין בק"ש ובתפלה עד שיטבול כדי שלא יהיו ת"ח מצויין אצל נשותיהן כתרנגולין ואחר כך בטלו אותה תקנה והעמידו הדבר על הדין שאף בעל קרי מותר בד"ת ובק"ש ובתפלה בלא טבילה ובלא רחיצה דתשעה קבין וכן פשט המנהג:
As translated by Sefaria:
All those who are impure read from the Torah, and read the Shema, and pray - except for the Baal Keri [he who has an emission] who was removed by Ezra from the rest of the impure people, and he [Ezra] prohibited him [the Baal Keri] from reading the Torah, reading the Shema, and from prayer until they immersed, so that scholars would not be with their wives like roosters. And afterwards they canceled this enactment, and returned it to the original law, that even the Baal Keri is permitted in Torah, reading the Shema, and prayer without immersion and without washing with nine Kabs of water, and such is the custom.
Go the ocean, which is as kosher a mikvah as they come, wearing a loose-fitting garment
Most men's mikva'ot are open (almost) 24 hours. This has the advantage of being able to use the mikvah during "off hours" when no one else goes.
As an example, a shul in my neighborhood has a small mikveh in its basement. I found that going on a weekday at the time that people in the shul daven's Shacharit was an ideal private time. I was the only one there. It's not a guarantee but it makes sense that if the mikvah is attended mainly by shul members (in this case, it is), then few people will be attending the mikva during davening time.
Another idea is to call the attendant and ask if they could open the mikvah just for that person, by arranging a mutually agreeable time. It's worth a chance asking.