Can this be a case of multi-class skewness?
Just telling the accuracy does not mean anything in classification problems. The first thing you must do is to calculate your baseline, that is, what is the percentage of your majority class? For the bar plot above it is difficult to measure, can you tell us in percentage, instead of counts? In this way we can assess better your results.

Also, have you plot a confusion matrix? In this way you can see where your model are getting more wrong and try to infer why this is happening.

And yes, since you have too many classes to predict and most of them are with low representativeness this will be difficult to overcome. Maybe you can try things such as Oversampling, Undersampling techniques considering one-vs-all approach. This is just an idea, I haven't yet encountering a problem with so many classes to predict.