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Does the obligation to recite one hundred Berachot apply even on Shabbat?
Yes. Although on Shabbat the Tefillot contain fewer Berachot, one must still fill the quota of 100 Berachot. On Friday night, one recites 11 Berachot during Arvit, and an additional 47 Berachot are recited during Shaharit, Musaf and Minha. One must eat three meals on Shabbat which adds another 18 Berachot (2= Al Netilat Yadayim + HaMotzi, 4= Birkat HaMazon), and there are few additional Berachot recited for Kiddush, HaMapil (if your custom is to say it with a Shem U’Malchut) and after using the restroom. Still, on an average Shabbat, one will find themselves about 18 Berachot short. Therefore, the Shulhan Aruch (OH 290:1) writes that one should eat sweet fruit and smell various fragrant spices to accumulate extra Berachot throughout the day. Bedi’avad (if one has no choice) one can rely on answering Amen to the Berachot of Keriat HaTorah and Haftara (an additional 27 Berachot). Getting an Aliyah or going up for Hazzan can also help. There is also an opinion that reciting the prayer of “Ein Kelokenu”, which has in it all the components of a Beracha, is equivalent to having recited 12, and some say 20, Berachot.