Agent Barry Tilly is the FBI Agent who was assigned to arrest Harry Dresden on suspicion of bombing his own office building. Dresden describes him as a slender little man with fish-white skin and ink black hair. Tilly's hand tingles indicating a minor talent probably augmenting his ability to tell when people are lying and help him be a great detective.
Tilly can hold a "heck of glare", that says he is willing and capable of doing bodily harm. Words aren't needed the "faint shadow of old Death in his eyes" is sufficient to cow his target. He also kicks Rudolph out of the interrogation room, saying he is "useless, unprofessional, and impeding the investigation."
Sometime in the past, Agent Barry Tilly met Karrin Murphy. Murphy identifies him as an aikidoka, and states that she has been to his dojo a few times to teach some practical application classes, while he has been to Dough Joe's Gym to teach forms and formal weapons classes. As such it could be assumed that Tilly is a peer to Murphy in regard to martial arts skill. Tilly and Karrin also seem to hold each other in enough regard that when Tilly says that Karrin backed Harry Dresden, he was impressed and by proxy had respect for Dresden.
In the series
In Changes, Harry Dresden meets Agent Tilly when he is fingered by Rudolph as the prime subject when his office's building is destroyed. Tilly does not believe that Dresden blew it up. Rudolph lied his ass off to Tilly's superiors to get Dresden here. Even though Tilly told Dresden he could call him Tilly, Agent or Agent Tilly, Dresden ignores all the options available and nicknames him Slim. Dresden seems to genuinely like Tilly and when they shake hands Tilly's hand tingles indicating a minor talent. Dresden believes that his ability probably augments his ability to tell when people are lying and help him be a great detective. As Dresden is leaving and Tilly asks for who really blew up the building he honestly processes the information given to him.
Later, Tilly had Susan Rodriguez in for questioning. Dresden went to FBI Headquarters to get her out. While there the Eebs and their troop of Red Court vampires attacked—they're apparently after Dresden, Susan (to stop them from their mission to save Maggie) and Rudolph (their loose-end patsy). During the attack, Karrin called out to him shouting Tilly which grabs his attention and Tilly automatically goes cool under the pressure. He's put in charge of Rudolph who lost it during the attack.