The Battlebabe's advance is available right away and you can decide who you want to be your Ally - that's what makes it valuable even though advanced Manipulate eventually becomes available. I played a Battlebabe and that was my first advance because I wanted my character's father to be special. Otherwise, he would have been viewed through the MC's crosshairs and possibly a Threat until I got five advances and had a reason to Manipulate him - and I would have had to get a 12+ for that to happen.

Also advanced Manipulate can very well lead to the end of the campaign - you are making more and more of the people around you genuine friends and removing them as Threats. You're establishing a status quo of sorts, since they're no longer targeted by the MC's crosshairs. It might be worth taking a look at the game and seeing if ending soon might be on the table, or maybe the Skinner is heading towards retirement and might take her Allies with her.

Part of the issue is one of MC/player expectations. Act under fire is only opaque if you as the MC are waiting for a player to say, "I 'act under fire' to..." - which to be clear you should basically never be doing. Your primary roll as MC is to determine when a PC's action (as described narratively in the fiction by the player) triggers a move and to call for the appropriate roll. As much as possible you want to abstract the move from the fiction such that your player isn't saying, "I 'go aggro' on this joker," but rather, "I stick my gun in his face and tell him to give me the Geiger counter" - at which point you (the MC) say, "Oooh, nice! Roll+Hard!"

In the context of the Battlebabe, act under fire is the move that is most often used when a PC is doing something daring, something where it feels like success shouldn't be automatic and/or some level of skill or chutzpah is required. It is most often the move that sets you up to be in a position to do some other move. So encouraging the Battlebabe to kick ass is best done by putting the Battlebabe in situations where kicking ass is appropriate.

That said, you need to take some care here, because while the Battlebabe is usually fantastic at starting trouble, not having a great Hard stat means they're often not so good at finishing the trouble they've started. Stand-up gunfights are for the Gunlugger. The Battlebabe excels at things that are not necessarily violent, but rather those things which are dangerous. No one is better at swinging across chasms, or scaling walls in the dark of night or tight-rope walking into the enemy camp. The Battlebabe is that rare person who can sneak past the guards unseen, dodge the enemy's strongest attack unharmed, slip a drug into someone's drink unnoticed, or run full-tilt through a minefield unscathed. If you present the Battlebabe with these kids of dangerous situations and call for roll+Cool to solve/get out of them, your players will catch on in a hurry.

A lot of new players in my games seem to pick the Battlebabe and then play cautiously and limply. I think part of it is that Act Under Fire is one of the more opaque moves when you're starting out. How do you recommend giving these players chances to breathe and kick ass?

I have to admit that Seize by force already in first edition is the part of rules which is conceptually hardest to swallow for me, as it seems to dilute the boundary between failure and success (you will get harmed no matter what).

Taking Harm is not failure. It is the price of success. Or rather it's the ante to even have a shot at succeeding in the first place. When things have devolved to seize by force or single combat, bullets are flying and the situation is already well and truly out of control. Harm is just what happens to you while you're trying to get yourself out of the mess.

Thank you both for the answers! I read the recommended thread.

I have to admit that Seize by force already in first edition is the part of rules which is conceptually hardest to swallow for me, as it seems to dilute the boundary between failure and success (you will get harmed no matter what). The direction in which 2ed went seems only to make it more pronounced. In some, not so rare circumstances, you cannot quite succeed and you will not quite succeed.