Persona
In Persona 3, SEES members utilize a special force of shadows known as Persona. They are reflections and masks of the true self which allow the user to overcome great obstacle. Mitsuru has two, Penthesilea and Artemisia. They are ice based as many empress arcana persona tend to be. In addition, both of her persona are notable high ranking females. They are queens and rulers, which help to promote Mitsuru's overall personality and ideologies as a "queen" or important woman. They were both strong in their own rights and I think that they both fit well with her. Unlike the other members of SEES, Mitsuru was not born with her ability to use Persona. She came into it after being subjected to experiments run by her grandfather's mad ideology. Mitsuru gained her persona as a means to protect her father. She volunteered to go to Tartarus with the group of scientists. When they turned to shadows and tried to attack her father, she summoned for the first time. Her dream has always been to fulfill her father's wish of ending dark hour.
Penthesilea
In Greek Mythology Penthesilea was an Amazon Queen; she served in the Trojan War as part of Troy's defenders. She wanted to die after killing her sister during a hunting accident but was unable to do so outside of the field of battle (as per her culture's identity). She joined the war for two reasons; one was to prove that the Amazonians could fight in wars and endure the hardships. The second was to atone for killing her sister. She promised to kill Achilles, but was unable to do so. She joined the Trojan War and on her first day of battle was defeated and killed by Achilles. It is said that Achilles felt remorse after removing her helmet. Some say that he fell in love with her the moment he killed her. There is much fragmented about Penthesilea and what happened to her, so there is not much known beyond her being part o the Trojan War and being an Amazonian Queen.
Mitsuru shares a parallel that she is a woman of power who desires to prove herself. In particular, Mitsuru comes into her persona by defending her father in Tartarus. She vows to protect him but is ultimately unable to keep her promise when Ikutsuki betrays them. Mitsuru also shares a parallel in the sense that she loses her desire to fight and is overcome with grief when her father is murdered. She loses her will to do anything and it is only through Takeba Yukari's friendship that Mitsuru is able to resolve to keep fighting. This resolve to keep moving forward, to avenge her father, to head back into battle is what causes her persona to metamorphosize. She returns to the field of battle stronger and more capable.
Artemisia
I assume that Artemisia is a reference to Artemisia I of Caria, who happened to be an ally and naval officer for Xerxes. She took the throne after her husband passed because her son was still too young to do so. She had a particular strength that won her Xerxes's trust and made her the only female commander of his campaign.
In the Battle of Salamis she cautioned against a naval battle because the Greeks naval force was much stronger than their own. She was the only one to speak against the particular battle, but Xerxes went ahead with it anyways. When nearly captured she attacked one of her own allies which led her enemies to believe she was either with them or that she had deserted her cause. In fact, some believe she flew two colors, Persian for when she attacked Greek ships and Greek when fleeing. This tactic shows some common sense in the idea that one would not attack their own ally. She was praised as being as good as any man by Xerxes. She was known for her cunning and intelligence.
Above all else, Mitsuru values intelligence. She will befriend the M/F protagonist only after they have reached the height of the intelligence attribute. I find it interesting that Mitsuru is also highly intelligent and values calm and critical thinking. She also serves as a sort of advisor to SEES which also fits with the original story of Artemisia in which she gives advice to Xerxes. She lives in a man's world in which she is actually at the top of many things (the heir to a family company, student council president, top of her class). Mitsuru consistently out-performs her peers, male and female, making her a force to be reckoned with. Her calm mind and ability to keep things going is what makes her a likely candidate and heir for Kirijo after her father passes away. She steps in and does what she needs to do.
The Empress Arcana
The Empress Arcana usually belongs to ice and healing persona. However, it is also used to represent women of power. In tarot, the Empress card symbolizes a great many things of which include (but are not limited too) mothering, abundance, material prosperity, and power. All traits that Mitsuru has shown. She acts as a sort of advisor and seems to be a safe haven for SEES. When Mitsuru is grieving over the loss of her father, the other members of the group have no idea how to approach her or cheer her up. In particular, Akihiko seems to be lost without her strong personage. She is their leader and I assume that in many cases, the protagonist defaults to her for advice or assistance. Rather, I suppose, that all things of SEES still go through Mitsuru.
Interestingly enough, in tarot, the Empress is associated with Isis, Yukari Takeba's Ultimate Persona. This could be a sort of hint for Mitsuru as to how important Yukari's friendship really is to her, although, I also wonder if this is an oversight by developers. Empress arcana is also associated with Demeter, the goddess of harvest and bounty. Empress often represents mothers, good and bad, or the demands of the real world. This is particularly fitting for Mitsuru who is often depressed or trapped by real world things and is unable to fully master them (rather unable to master them by herself). The Empress arcana notes women of power as being both kind and motherly but also harsh and unforgiving as Demeter was when her daughter, Persephone, was taken. The duality of empress lends to both giving and taking life which might be why persona of this attribute are able to attack and heal.
The Ice Queen
With everything that has been said, I feel there is just one more thing to really look into. Mitsuru's innate element is ice. She often comes off as cold and aloof. She seems to be so far out of the reach of her comrades, I think that there is loneliness on both sides. I think, in part, this is due to Mitsuru's upbringing which has cultivated her to be strong and independent, if not wary of others. She is the heir to a major company and she needs to be a role model to those around her. She gets very caught up in being the "ideal" that I find she can be icy, but not because that's exactly how she is. She wants friends and people to rely on but she is often put into the position of "for duty and family" or "for myself and friendship" in which she usually chooses duty and family. It is only after the death of her strict father and the understanding of Yukari that she begins to open up. Although, Mitsuru still drives a very hard line of being friendly and cold. Being friendly only to those who have won her heart and respect and punishing all who cross her (including friends who might have gotten the wrong time in the hot springs - I'm looking at you Junpei, M Protagonist, and Akihiko!)!
In fact, the M or F protagonist can befriend Mitsuru (the male is able to date her) and help her decide some things about her own life and how those decisions can be good for Kirijo and her without being detrimental. Through her friendships she is able to be a stronger and more capable leader; this also makes her a much more dangerous enemy. I think that as her element is ice this means she can be cool and refreshing (healing) or harshly cold (execution).