I'll do't".
The sum of what has been said may be given in the words of Archdeacon Nares:
"There is no doubt that eisell meant vinegar, nor even that Shakspeare has used it in that sense; but in this passage it seems that it must be put for the name of a Danish river.... The question was much disputed between Messrs. Steevens and Malone: the former being for the river, the latter for the vinegar; and he endeavored even to get over the drink up, which stood much in his way. But after all, the challenge to drink vinegar, in such a rant, is so inconsistent, and even ridiculous, that we must decide for the river, whether its name be exactly found or not. To drink up a river, and eat a crocodile with his impenetrable scales, are two things equally impossible. There is no kind of comparison between the others."
I must confess that I was formerly led to adopt this view of the passage, but on more mature investigation I find that it is wrong. I see no necessary connection between eating a crocodile and drinking up eysell; and to drink up was commonly used for simply to drink. Eisell or Eysell certainly signified vinegar, but it was certainly not used in that sense by Shakspeare, who may in this instance be his own expositor; the word occurring again in his CXIth sonnet.
"Whilst, like a willing patient, I will drink
Potions of eysell, 'gainst my strong infection;
No bitterness that I will bitter think,
Nor double penance, to correct correction."
Here we see that it was a bitter potion which it was a penance to drink. Thus also in the Troy Book of Lydgate:
"Of bitter eysell, and of eager wine."