After an hour of Googling and trying things I think I have found a solution.
IIOMetadata iiom = ir.getImageMetadata(i);
TIFFDirectory dir = TIFFDirectory.createFromMetadata(iiom);
TIFFField fieldXRes = dir.getTIFFField(BaselineTIFFTagSet.TAG_X_RESOLUTION);
TIFFField fieldYRes = dir.getTIFFField(BaselineTIFFTagSet.TAG_Y_RESOLUTION);
int xRes = fieldXRes.getAsInt(0);
int yRes = fieldYRes.getAsInt(0);