Its domain is more serious crimes, such as murders, bodily harm, economic, financial and property criminality with very high damages or with a particularly qualified manner in which the crime was committed.
This is a list of the serious crime:
3)economic, financial and property criminal acts.
4) qualified manner crimes
"with very high damages" further describes the group (3)
the "or" begins the last of the series. A "particulary qualified manner" probably mean those with a specific MO, like a serial killer or terrorist cell group with a specific plan.