Oh, he's tried. Castle went back into Johanna's file in the first season and linked her murder to three other killings, meaning it wasn't a random act of violence, but a planned hit. His discovery put a rift in his relationship with Beckett in the finale since the detective explicitly told him not to get involved. It was Very Awkward when he returned in Season 2, but then everyone forgave him.
5. What happened in Season 2 that made everyone forgive him?
In the episode "Sucker Punch," Beckett arrested Dick Coonan, the assassin hired to kill her mom. Unfortunately, Coonan tried to escape the precinct at the end of the episode, and Beckett was forced to shoot him to save Castle's life. A seriously sad scene followed where she tried to revive Coonan's lifeless body to find out who ordered the hit on Johanna. One good thing to come from this is that Beckett told Castle she wants him to be there when the case is solved, further strengthening their bond.
6. Has there been any progress?
Has there ever! This season in "Knockdown," Beckett and Castle went to a diner to meet with a dude named John Raglan, the cancer-stricken lead detective on Johanna Beckett's murder case. Raglan quoted some Dickens and said he made a bad mistake 19 years ago that triggered a domino effect. Then, he was shot by a sniper from an apartment building across the street before he could tell them more specifics about these dominoes.
7. Wait, so twice someone has been shot before they could tell Beckett the 411 on her mom's murder?
8. The rest of this story is complicated, isn't it?
You bet. Deep breath, and here we go. Montgomery took Beckett off of the Raglan case after she threw a creepy drug ring leader named Vulcan Simmons into a mirror. Johanna Beckett ran an anti-drug campaign in Vulcan's neighborhood back in the day, and Beckett first suspected that Vulcan hired Dick Coonan to carry out the hit and then had Raglan, his NYPD connection, bury it. Not so much. Ryan and Esposito actually linked Raglan's murder to a guy named Hal Lockwood.
9. So, Lockwood did it?
Yes, but hold on a sec. Beckett and Castle conducted their own separate investigation at her apartment, natch. They found a roll of film among Johanna's possessions with pics of the alley where she was killed. In his Castle-y way, Castle linked this to FBI Agent Bob Armen, who was killed in the same alley as Johanna nineteen years ago when he was working undercover at an old mob hangout. John Raglan arrested mob enforcer Joe Puglatti for Armen's murder, and he plead guilty. But after visiting Pulgatti in prison, Castle and Beckett figured out that NYPD officers — including Raglan and Gary McCallister — were actually kidnapping mobsters for ransom at the time. When Armen was accidentally killed during one of these attempted kidnappings, Raglan pinned the crime on Pulgatti as a cover-up. Johanna Beckett and several of her colleagues tried to put together an appeal for Pulgatti years later. Dick Coonan was then hired to kill all of those people, and Lockwood was hired to kill Raglan later on. McCallister confessed the mob stuff to Castle and Beckett, but said he didn't hire Coonan or Lockwood. That's someone else, a sleeping dragon.
Meanwhile, Ryan and Esposito were kidnapped and tortured by Lockwood, and Castle and Beckett kissed right before saving them (to distract a guard, sigh). Lockwood was arrested, and Beckett promised to visit him week after week in prison until he tells her who is behind all of this.
Mmm, no. We don't even know what Hal Lockwood's real name is, because it's definitely not Hal Lockwood. But they're inching closer!
11. Why is this case so important?
Aside from the obvious, Johanna Beckett's murder is one of two continuous and unresolved storylines in the show, the other, of course, being the Castle and Beckett romance. This is meaningful because Beckett is essentially trapped between the thing that brings her the greatest sadness and the thing that could potentially bring her the most happiness. Interesting that the first time the two shared a kiss is also when they got closer to solving the murder. It's so deep, we're almost drowning in it.