Everyone likes to blame Kate for all the deaths in Army of the Dead, but even in the worst case scenario she's responsible for two deaths. I'm just going to consider who can be blamed for everything for fun.
The players are: Scott, Kate, Cruz, Vanderohe, Peters, Dieter, Guzman, Chambers, Lilly, Martin, and Cummings. I'm not going to entertain the concept that Bly is responsible because he offered the mission, or Scott because he accepted. Yes, no one would die if Scott declined the mission, but everyone here is an adult making their own decisions.
Chambers - First to die, so she doesn't get much chance to get anyone killed. She's partially responsible for her own death (if you think someone is up to something nefarious, it's not incredibly wise to tip them off that you're coming for them when they have an opportunity to do something nefarious to you). Of course, Martin is primarily to blame for her death.
Cummings - First to be removed from the group, and never gets the chance to let anyone down. He technically kills Daisy, but that's a direct result of Lilly's actions, not Cummings'.
Vanderohe, Cruz, Dieter, and Guzman - Professionals who stay on mission and get no one killed.
Lilly - Lilly gets Burt killed right off the bat. The mission wouldn't have moved forward without this sacrifice, but it doesn't change the fact. This also indirectly gets Daisy killed later. She supports Martin in dangerous actions, but doesn't realize how dangerous he's going to be, so isn't responsible. She was also arguably too honest with Kate multiple times, which led to Kate joining the group, then departing it later. This was information that was only likely to be misused by Kate, however Lilly is only directly responsible for one death.
Peters - Mostly a professional who stayed on task, but by leaving Scott then coming back for him instead of simply waiting as long as she could, she created a short delay that allowed Zeus to catch up to the helicopter. Zeus' arrival led to her wound, which prevented her from keeping the chopper under control, causing it to crash and kill herself. This also enabled Scott's death at the hands of Zeus, and potentially killed Geeta in the crash (though her status remains unknown). Peters is responsible for two deaths.
Scott - A professional who stays on task, until his daughter goes missing, at which point he had Peters head to the Olympus. This action put Scott and Peters at risk, though as a result he was able to save Kate and Geeta without getting anyone killed (though Peters fiddled with the process and people died anyway).
Kate - Kate just tagged along for most of the mission. When it came time to act, she took responsibility for herself and didn't involve anyone else. As Scott warned her ahead of time, though, he wouldn't just leave her, so she put him at risk. If Scott and Peters hadn't gone after her, they wouldn't have died, but it was arguably more Peters' fault for leaving them, and Scott's fault for going after her when he could have left her. Of course that'd never happen, but it was, in fact, Scott and Peters who made their own decisions.
Martin - Right away he gets Chambers killed, obviously. Then by taking Athena's head he angered the horde, which would not have otherwise attacked. As a result he, Scott, Cruz, Dieter, Lilly, and Peters died. The only death he wasn't directly responsible for was Cummings'. Martin is responsible for seven deaths.