I have been waiting to see a TAS of
Ikari Warriors for a long time. I recently completed a non-tool-assisted play-through of the game without using the A-B-B-A cheat code. You can view and/or download the play-through here:
http://www.archive.org/details/IkariWarriorsfullgameDVDRW
For TAS purposes, you probably shouldn't use any tanks. Once you obtain the super-speed power-up in the first stage, you will move more quickly on foot than in a tank.
Yes, obtaining a heart will allow you to carry your power-ups from one stage to the next. But this will count as using your heart, so you will have to obtain another heart in the next stage.
Using the chopper might be faster during sections where you have to cross water, but I haven't tested this.
Edit: By the way, I obtain the first super-speed power-up at 6:59 of the video. I think that this is the first super-speed power-up in the entire game, but I could be wrong.
Also, you'll probably want the knife power-up for the TAS. The knife allows you to kill enemy soldiers by touching them. I obtain the knife at 7:51 of the video.