Here is one of my favorite catch-up strategies for the highest level. AI's don't tend to balance city value with defence well. Thusly, huge cities will have the same defence as small cities. You, the failing player, can take advantage of that. Firstly, select a target city. It should be the largest city of a colony far from your borders. This is so they cannot retaliate. Then, temporarily empty ships whose cargo space is about 6 more than the target city's population. Bring this fleet and a force of 3 soldiers and one cannon to the borders of the target city. Wait for them to "shuffle" the troops so there are as few as possible inside. (Yes, they do this) When there are the fewest troops and the most civilians, attack. This is easiest and best if you have Amphibious. Capture the city, but leave your ships outside in case you lose it. If your attack is a surprise like it should be, you won't lose it. The turn rebellion ends (and this is the fun part) move your ships in and just take everyone and everything except for one guy, a Petty Criminal or Indentured Servant ideally, and your troops. Sail your new, free specialists and goods away to your home colony. Having lost their best city, the AI should sue for peace. Repeat as needed. This strategy also works better as difficulty goes up, because the colony is more developed. I use this to great effect in the AOD2 mod to combat the superai there who are, unfortunately for them, not superpowered. This works for me, hope it helps you!