He is in love with himself. In Christian morality it is the opposite of loving one's neighbour, and hence a sin against Christ's greatest commandment.
My entire soul and every single and individual part of this
sin = the sin of self love.
no remedy - in a general sense it means 'no cure', and figuratively, no way of putting the matter right, no alternative.

Methinks = an old word meaning 'I think that...'
gracious = full of grace, beautiful.
No shape so true - no bodily shape as perfect, right, proper, correct
As = to the extent that, so that.
I all other in all worths surmount = I surpass everyone in any and every quality. other is an old plural form. We would say 'others'.

tanning in this case does not refer to a sun-tan, but to the operation of tanning or curing leather, which was done in a