I'm playing as Riftborn and Σ has "power to shields" and "hard target", while i have "turtle", "power to shields" and "get lucky" active. Is it supposed to be like that?

Sorry no one jumped in to help  sooner..

These are different battle tatic cards that can be activated. You can unlock more tatic cards and slots be researching them in the military section of the tech.. web. When you get the research for increasing the size of your fleets (if i recall) but there are 2 CP increases for your fleets they look like radar dishes. They increase you tatics slot by 1 each time. Plus you can unlock different battle tatics in the military tree as well they look like cards.

To switch battle tatics go to the fleet tab at the top of the page and when the fleet tab is opened on the left side there is a bunch of sub tabs and one of them is manage tatics. There you can see all of the different tatics you have and can drag and drop different ones into your active slot at the bottom. Every 10 turns you can switch up your tatics for free otherwise it costs influence i believe.

Some heros have different abilities that can be used in space battles that you dont need to add to your battletatics slot. Once they are unlocked when the hero is in combat then you can use the heros battle tatic as another option (only visible for the fleet that they are a part of).

I hope that i answered your question alright. Again sorry for the delay. If you have any further questions feel free to shoot me a message and I will answer your questions to the best of my abilities.

-Mr. Tyco