You gotta use Rage Mode to get into melee, or hit them with a Takedown Move. Normal attacks will take them down to 1 HP, but then they stop hurting them. No that doesn't make any sense.
If you can't do takedowns yet, and you aren't good in melee, soften them up with some charged shots before you close in, since they can hit pretty hard.
The Bridge level was the worst one in the entire game. Since it's supposed to serve as a morale tutorial, there's a lot of really heavy scripting, that messes with the moral meter, so it doesn't act anything like the actual game.
Which is stupid; the moral meter is the absolute crux of the battle system, and the flawed understanding of how it works, that the tutorial gives you, can cost you a lot of battles later on.
The whole game is really hamstrung by stupid decisions like that, but it has it's moments.
I still look back fondly on memories of ripping a battle rhino's skull out of his face and then throwing it through a battleship.