I find that it's easiest to think of the different intervals on the fretboard in terms of diatonic "distances". Diatonic distances are like diatonic intervals, the major third and perfect fourth etc. of usual music theory, except that they are zero-based: a string forms a unison with itself, so it's at diatonic distance zero. Numbering the guitar strings from the sixth (lowest) to first (highest), the diatonic distances that are crossed in the conventional tuning are 3-3-3-2-3. Just add one to the sum of distances and you get the figure for the corresponding interval: so the 2nd and 1st string form a fourth, 3rd and 1st form a major sixth (as do the 4th and 2nd string), etc. You really don't need any kind of brute force memorization.
Then you can just use solmization in your mind to figure out how to build any scale pattern on the fretboard regardless of key, keeping in mind that e.g. ut-fa is always a perfect fourth, ut-mi a major third etc. and that mi-fa is always the semitone interval. (There is no ti in historical solmization, you just sing sol-re-mi-fa for the upper tetrachord then pick up again with re-mi-fa etc.) Memorization comes most easily from repetition, the deliberate effort should go towards figuring out the underlying patterns and how to think of them most intuitively and musically.
(BTW, solmization is also very helpful in making musical sense of isomorphic keyboards, which much like the guitar fretboard are essentially non-diatonic. It helps you keep track of where the semitone intervals are in a musical line, since they will always be associated with mi and fa.)