Here are the few facts you have to understand.
She is Boss: Regardless of whatever the other employees may be thinking about her, higher management trust her and placed her in a senior position. That means she has some qualities or skills which are very valuable to the organization. You should respect that.
Your work should first be recognized by her: Another thing you should be aware of is that she is the first person whom you should impress with your work. She reports to the organization about you and your work. Even if she is wrong in her judgement of you or your work, her opinion is valued by higher management more than yours is.
Bosses also have weak points: Not every person is good at eiquitte, diplomacy and communication. Maybe your boss is weak in these areas. However, she might be good in other areas. You should look for those.
A team is stronger than individuals: Many managers focus on teams rather than individuals. Not all team members have all the skills at the required level. But if a team needs to achieve certain tasks managers select a team with the people who are strong in different areas and thereby make the team strong enough to achieve the task together. In some teams, the lead may not be technically strong enough but strong in soft skills. If the team requires both technical and soft skills to achieve something, managers select a team with one member who is strong at soft skills and another member who is strong in technical skills.
Below are the points that helps you to support your boss:
Understand Your Boss: Try to understand your boss. Understand their targets, their strengths, their weaknesses, their priorities and where they are in the process of achieving their targets, what are their struggles etc. This will help you to support her better. Try to figure out where you can help her.
Build Trust: Trust is very important. Once you have built trust with her then you will be good. You can support her more and more and she can in turn support you. This may be difficult to achieve, but it is good for the team, for you and for her also.
Help her with her problems and weaknesses: If she has any weak points to do certain tasks, like conveying message softly, scheduling things or planning things, you should proactively help her. Politely and proactively offer your help - like managing her schedule or reminding her about other priorities, taking care to communicatie efficiently etc.
Make her rely on you for difficult tasks: If the boss is weak in one area, it is a very good opportunity for you to get tasks in that area and get things done. In this way you will get a good rating from your boss. Take up those activities and do the good work, so that she will rely on you further.
Try to become a bridge between your boss and employees/team members: Finally as a assistant manager try to become a bridge between her and the team. In this way both she and the team rely on you, and you will become the most valuable member of the team.