Lets look....
Shooting: Military base at Fort Hood, Texas
Legally purchased with a federal background check
Shooting: Gabrielle Giffords
Legally purchased with a federal background check
Shooting: Movie theater in Aurora, Colorado
Legally purchased with a federal background check
Shooting: Sikh temple in Oak Creek, Wisconsin
Legally purchased with a federal background check
Sandy Hook Elementary school in Newtown, Connecticut
Legally purchased with a federal background check by parent, weapons stolen after he murdered the parent
Washington Navy Yard in Washington, D.C.
Legally purchased with a federal background check, prevented from buying a pistol due to him being out of state under existing federal law.
Military base at Fort Hood, Texas
Legally purchased with a federal background check
Those are just the first several, notice a pattern, legally purchased after passing the federally mandated background check. I think we need to strengthen the existing system myself as a good start.