Saints Row IV

Further to Mobius' excellent guide, I thought I'd add some clarification on when this unlocks, because the achievement description is misleading.

Just as in Saints Row: The Third, the Steelport map is divided into four districts:
Top Left: Stanfield
Bottom Left: Carver Island (which includes the smaller island between Stanfield and Carver Island)
Centre: Downtown (both islands)
Right: New Colvin

This achievement unlocks when you've completed all of the open world activites in two of these four districts, rather than when you hit 50% completion for the whole map.

Open world gameplay consists of all 117+ activities that you can complete to gain control of hoods. If you open your map, every area that is colored in purple is owned by the Saints and will not contain any open world activities to complete (pre-DLC anyway; instances of "Genki Holiday" and "Naughty or Nice" can and do pop up within controlled areas, but also do not count toward this achievement.)

Some activities are not available until after completion of story missions and the parallels are always obvious. For example, Mech Suit Mayhem does not unlock until completion of the mission Zero Cool where you are operating a mech suit. The final locked activity is Superpower Fight Club, which is a required objective in the story mission Anomalous Readings.

At the top-left corner of the map screen is your progress toward this achievement, referred to within the game as the amount of the simulation you have "hacked". This percentage is only an overall statistic when the cursor is hovered over water though, since hovering over a landmass will give you statistics for just that island. However, this achievement is marked as buggy because it only unlocks when it feels like it. I did not receive this achievement until 97% hacked (and 68% game completion).

The activities are (followed by how many of them exist on the map):
Store hacking x34
Flashpoints x32
Mayhem x13 (4 normal, 3 telekinesis, 2 tank, 2 mech suit, 2 UFO)
Blazin x9
Rifts x8 (3 speed , 3 platforming , 2 telekinesis)
Hotspots x6
Tower climb x5
Insurance fraud x4
Genki's Mind Over Murder x3
Superpower Fight club x3
Chop shop x?
Assassination x?
Virus injection x?