@MariosOreo one-hot won’t help, as “each Image can be assigned to 1 or more labels”.
This is not only multi-label classification, but also multi-class, which is harder. Benchmarks which aim at solving this type of classification are for example Microsoft COCO, Open Images, PASCAL VOC, and many others.
I think you can use cross entropy as loss, to be verified.
For metrics you should check precision and recall 2 as well as F1-score 1, which is the harmonic average of P and R for more stability than just taking the mean.