Trigz -- Arrest Made In Tattoo Artist's Murder

Police finally busted a man for allegedly gunning down Chris Brown's tattoo artist, Trigz ... TMZ has learned.

LAPD arrested Robert Falcon on Tuesday for the murder of Trigz earlier this month. The tattoo artist -- who worked with tons of music celebs -- was shot outside the Black Derby Smoke Shop in North Hollywood.

As we reported ... police say Trigz and Falcon had gotten into an argument, which eventually ended in gunfire. Falcon was booked for 1 count of murder and his bail was set at $2 million. He's still in custody.