The legend of Ymir Fritz has been the lynchpin in the Attack on Titan universe. Once a young girl, Ymir Fritz, came into contact with an unknown creature; this creature allowed her to transform into the first Titan. Like most historical events, Ymir Fritz's story was transformed into that of a legend. The Eldians viewed Ymir as a Goddess. Her powers were so great that she cultivated that land, built bridges and roads. The narrative of a Titan Goddess changed after the collapse of the Eldian Empire. Freed from the ruling of the Eldians, the Marleyans built a new empire, Marley.
According to the Marleyans, Ymir made a deal with the Devil of All Earth to obtain her Titan powers. With her Titan abilities, Ymir was able to help the Eldians defeat and enslave the Marleyans. These two legends of Ymir Fritz differ significantly, but one element of the story never changes. After thirteen years of having the Titan power, Ymir dies. After her death, Ymir's soul is split into nine pieces, specifically the Nine Titans, each possessing unique abilities.
The Founding Titan
The first of Attack on Titan's Nine Titans is the Founding Titan. The Founding Titan can be considered the most powerful of the group, controlling Titans. Previous holder Karl Fritz used this power to build the three walls that protect the humans on Paradis Island. Using millions of his subjects as Titans, Karl Fritz created walls of Titans ready to flatten the Earth if necessary. If that wasn't enough, the Founding Titan also can alter the memories of the descendants of Ymir. This gave Karl Fritz the power to wipe the memories of all the Eldians within the walls. These powers can be used both in Titan and human form, making this Titan's powers extraordinary.
The problem with the Founding Titan is that only those of royal blood, the Frits/Reiss families, can use its power. Though if someone were to inherit the Founding Titan outside of the royal family, all they need to do is tough someone of royal blood. This is demonstrated when Eren Jaeger unknowingly used the Founding Titan's power on Dina Fritz's Pure Titan. After striking Dina's hand, Eren commands the Titans around them to devour her body.
The Colossal and Armored Titans
The more recent inheritors of these Titans are Bertholdt Hoover (Colossal Titan) and Reiner Braun (Armored Titan). Both men are scouts from Marley to obtain the Founding Titan and destroy those within the walls. When it comes to the overall abilities of these two Titans, both Bertholdt and Reiner use them to their full potential. In the case of the Colossal Titan, Bertholdt has mastered the ability of fast transformations by utilizing the large amounts of steam his Colossal Titan produces. On multiple occasions, Bertholdt will use the steam from his Titan to distract the soldiers or an incredible blast to throw them off the wall. Most important of all is the size of the Colossal Titan, towering over the wall; the Colossal Titan has the power to look down on most all Titans.
On the other hand, the Armored Titan is covered in platted armor, allowing Reiner to burst through the gates of wall Maria. With strong armored plates, it's nearly impossible to penetrate the Armored Titans' skin, and any exposed locations can be covered with the hardening ability. Though like the Colossal Titan, the Armored Titan can't move as fast due to the plating on its body. Regardless of these obstacles, Reiner held his own when fighting against Eren's Attack Titan.
The Cart and Jaw Titan
The following two Titans might not compare in strength to the others, but in speed and endurance, none compare. The Cart Titan is a quadrupedal Titan allowing its body to carry supplies and have great speed. This speed is displayed by Pieck's Cart Titan when she saved Zeke from Levi. On top of all this, possessors of the Cart Titan can stay in their Titan form for extended periods. Pieck had stayed in her Titan form for as long as two months. This resulted in Pieck walking around on all fours and needing a crutch.
Similar in speed is the Jaw Titan, the smallest of the Nine; the Jaw Titan is singular in its speed and agility. Locations like forests and cities are the best place for Jaw Titans to fight and show their mobility, but compared to other Titans, their strength is lacking. The main ability Jaw Titans possess is their incredible bite. Ymir uses this to bite through the napes of Pure Titans on more than one occasion.
The War Hammer and Female Titans
The War Hammer Titan has been in possession of the Tybur family since King Fritze abandoned the Eldian Empire. Since then, this Titan has been used to assist the Marleyan Empire. The War Hammer Titan is unique compared to the other Titans because of its ability to use hardening to produce weapons or send hardened spikes shooting from the ground. The War Hammer Titan can also be controlled remotely if this wasn't enough. By using a cable connected to the user's crystal encased body, the War Hammer Titan can operate without the user in its neck.
The Female Titan also has an unusual ability. Like the Founding Titan, the Female Titan can attract Titans to her location, but she doesn't control them. When they arrive, the Pure Titan will devour the Female Titan's body. Annie Leonhart uses this technique to escape from the scouts. The Female Titan also can harden different parts of its body, allowing for strategical attacks, or protecting the nape of the neck.
The Beast and Attack Titans
The last two Titans are the Beast Titan and the Attack Titan. The Beast Titan is close in power to the Founding Titan to control and create new titans. Zeke Jaeger, the current holder of the Beast Titan, does this throughout the show. Zeke Jaeger's Beast Titan also shows hardening and powerful throws. Something Zeke uses when attacking the scouts with a ball of rocks that scatter over the field.
With so much power in the Beast Titan and the other eight, it can only be assumed that the Attack Titan is just as powerful. In reality, the Attack Titan doesn't have any special abilities like the other eight. Though something fans see from all the inheritors of the Attack Titan is their drive to fight and never give up. Perhaps the Attack Titan's abilities aren't physical but mental. Much like Eren's drive to escape the contain meant of the walls, the Attack Titan refuses to give up.