Shulchan Arukh, Orach Chayyim 124:4 says:
כְּשֶׁשְּׁלִיחַ צִבּוּר חוֹזֵר הַתְּפִלָּה, הַקָּהָל יֵשׁ לָהֶם
לִשְׁתֹּק וּלְכַוֵּן לַבְּרָכוֹת שֶׁמְּבָרֵךְ הַחַזָּן וְלַעֲנוֹת
אָמֵן; וְאִם אֵין ט' מְכַוְּנִים לְבִרְכוֹתָיו, קָרוֹב לִהְיוֹת
בִּרְכוֹתָיו לְבַטָּלָה; לָכֵן כָּל אָדָם יַעֲשֶׂה עַצְמוֹ כְּאִלּוּ
אֵין ט' זוּלָתוֹ, וִיכַוֵּן לְבִרְכַּת הַחַזָּן. יֵשׁ
אוֹמְרִים שֶׁכָּל הָעָם יַעַמְדוּ כְּשֶׁחוֹזֵר הַשְּׁלִיחַ צִבּוּר
Summary / translation:
During the chazan's repetition, the cong. should be quiet and concentrate on the blessings that the chazzan recites and answer "Amen". If there aren't 9 people concentrating on his blessings it is close to his blessings being in vain. Therefore, each person should pretend that he is among the necessary 9 people ...
I.e. the above emphasizes the importance of every person listening to the chazzan and answering "Amen" even if there are far more than 9 people. You have to hear the chazzan no matter what.
It's unclear from your question as to why you can't hear the chazzan. If every else is schmoozing, then, unless the Rabbi takes control and makes them stop, it is very difficult for you to request it. Trust me, I've been yelled at numerous times for asking even 1 person to be quiet! (Long, sad story!). In that case, by all means, find a quieter shul.
If the shul is quiet, but you're too far away from the chazzan to hear him, can't you request a seat closer to the chazzan? I find it hard to believe that no one would accommodate your request. Even if you have to stand the whole time or most of the time, this should be possible.
If you're hearing impaired, that's another story. In many cases, you may actually be exempt from having to hear the chazzan, anyway. (As for hearing the shofar via hearing aids and implants, there's a pamphlet discussing these issues. Not a simple answer.)
I also assume that if you can't hear the chazzan, perhaps, you can't hear the shofar sound, either. That would be a bigger problem, as hearing the shofar on Rosh Hashanna is a Torah requirement. If the shul is that noisy that this is a problem, then, it seems that you definitely need to find a different quieter shul.