This achievement can only be earned in the Strategy Game, not the Campaign.
Start a strategy game with the following settings: Captured Islands Count (Few), Enemy Strength (Strong) Startup Resources (High), Islands Output Rate (High). You will start with three islands. Provision up as desired and start going to small islands on the map (while the island placements are random, the individual islands themselves are exactly the same layouts as in the campaign). When you find one that is listed as Deadly (press on the strategic map to see the rating), capture it. Deadly islands can be quite tough, so save frequently. When hacking the command center, save just before completing the hack. Reload that save 24 times and you will have all three of the "Balls of Steel" achievements.
Note that this achievement does not stack with the various "Bunker Buster" or "Iron Fist" achievements. However, the settings provided will likely create a game with both Deadly and Very Strong islands, so you can use the same game for those captures.