If Al Achilat Matzah is recited on the Mitzva of the Torah to eat Matzah on the night of Pessach, why don't we say it also during the 7 days of Pessach? As it is written "7 days you shall eat Matzot" Shemot 12:15. Isn't that a mitzvah to eat Matzah the 7 days of Pessach?
The Talmud (Pesachim 120a) teaches that while eating matza is obligatory on the first night of pesach, on the latter 6.5 days doing so is optional, not obligatory. The same rule applies to eating in the sukkah (Sukkah 27a). Regarding your question about the blessing:
The Baal HaMaor (Pesachim 26b) answers that since on the latter 6.5 days of pesach you don't have to eat matza if you don't want to but could subsist on fruits and vegetables, we don't say a blessing on eating matza (unlike sukkah where you can't go all week without needing a sukkah at least for sleeping).
The Sefer HaIttur (135a) answers that on the latter 6.5 days of pesach there is only a negative command against eating chametz that is at play when you eat matza and we don't say blessings on fulfilling negative commands (unlike sukkah where there is a positive fulfillment all week).
As @DoubleAA pointed out, Chazal explain that there isn't an obligation to eat matzah all seven days. However, your question may be coming from what the Mishnah Berurah (475 § 45) brings in the name of the Vilna Gaon, that you fulfill a mitzvah if you eat matzah during the seven days of Pesach, just there's no obligation.
This comes from Ma'aseh Rav § 185:
שבעת ימים תאכל מצות כל שבעה מצוה ואינו קורא לה רשות אלא לגבי לילה ראשונה שהיא חובה ומצוה לגבי חובה רשות קרי לה אעפ"כ מצוה מדאורייתא הוא
In the newer editions of Ma'aseh Rav, they bring the sources @DoubleAA brought why there is no blessing on matzah all seven days. However, at least some of those sources seem to understand that there is no mitzvah to eat matzah on the other days (see Birkei Yosef Orach Chaim 475:6 who discusses if the Ba'al HaMeor holds that you fulfill a mitzvah on the other days or not). If so, why is that according to the Vilna Gaon there isn't a blessing, since there is in fact a mitzvah?
Indeed, they bring from the Sedei Chemed (Ma'aracha Choshen Mishpat 14:10) that there are those who are accustomed to in fact make a blessing all seven days. Also, Rav Shlomo HaKohen from Vilna wrote a letter to the Sedei Chemed saying that according to the Vilna Gaon, there should be a blessing (but writes צ"ע). They also bring that there's a letter from the Netziv that discusses similarly.
In the end, they bring from Teshuvos Maharsham 1:209 that even according to the Vilna Gaon there's only a blessing the first night.
I looked up the Maharsham, and he brings that the Teshuvos Chasam Sofer (Yoreh Deah 191) brings from the Chizkuni like the Vilna Gaon, that there's a mitzvah all seven days, just not an obligation. Nevertheless, there isn't a blessing.
שיטת החזקוני על התורה דמצוה איכא באכילת מצה כל שבעה אע"ג דהיא רשות ואי בעי לא אכיל כלל ומש"ה אין מברכי' כל ז' על מצה מ"מ אי אכיל מצוה קעביד
He says the reason is like @DoubleAA brought, that since a person could get away without eating matzah the other seven days, there isn't a blessing. Nevertheless, if they do, they fulfilled a mitzvah.
The Maharsham also says the Ibn Ezra (Exodus 12:15) also held that there's a mitzvah all seven days. However, he doesn't say anything about the Vilna Gaon making a blessing or not.
Indeed, R. Chaim Ben Avraham of Kraz writes in a responsum (Pe'er Eitz Chaim #8) that one should recite a blessing of al achilat matzah for all seven days of Passover:
ולפי זה יש ללמוד דצריך לברך על מצוה זו של ז' ימים ויכול שפיר לומר וצונו כדכתי' שבעת ימים תאכלו מצות
See there at length where he argues that it is a full commandment to eat matzah all seven days, though it is of a different nature than the commandment to eat matzah on the first day.1 He adds that the poskim who say not to recite a blessing hold that it is not a commandment at all:
והפוסקים כתבו דאין לברך עלי' ע"ש אלא דזהו לפי שיטתן דלא אחשבו' למצוה כלל
He then adds that his approach is correct l'halacha and one can rely on it to make a blessing, but one who is not so convinced can rely on the prevailing custom to not recite a blessing:
אבל לפי דברינו הנ"ל ודאי מצוה גמורה היא וצריך לברך עליה על אכילת מצה בכל יום ויום כמו בלילה הראשונה וכן עיקר לדינ' ולמעשה ראוי לנהוג כך מי שאין דעתו יפה וחזקה כ"כ לסמוך על דברינו הנ"ל והלכה זו אכתי רופפת בידו ילך אחר המנהג ופוק חזי מאי עמא דבר שלא לברך
1. To briefly summarize, he explains that the commandment on the first night is to eat matzah for the inherentness of matzah, whereas the commandment for the rest of the holiday is to eat matzah to show that you are not eating chametz. Based on this distinction he lists various situations where one would be obligated in the first-night matzah but could exempt himself from the rest-of-the-holiday mztzah.