How does one parse 'woe betide'?
In the phrase, "woe betide", the verb "betide" is in the subjunctive mood. This is one of the left-over uses of the present subjunctive in fixed phrases. It means "may woe betide", like "long live the king" means "may the king live long".
According to the OED, betide meant happen or happen to. It was a regular verb conjugated like other verbs. However, nowadays the only place we see it used is in the expression woe betide.