This is an example of Drayton’s practice of taking an adjective that already exists, in this case ‘mountainous’, and modifying it to produce a new word that is both different enough to sound poetic and at the same time evokes a familiar concept. Other instances of this include ‘affrightedly’ (12.294), ‘burliness’ (8.382) and ‘spiceful’ (5.312).
The strange thing about his usage of ‘mountainously’, describing the Chiltern Hills, is that it is neither truly literal nor figurative. The Chilterns are not mountains, and yet they are more like mountains than, say, waves or the night, which are the kinds of things to which the adjective has been applied by later writers. There is possibly the sense that Drayton is so impressed by the English countryside that to him, even its hills are like mountains; however, ultimately the reasoning behind this usage remains unclear.