Given Sequence: $A\_BCD\_BBCDABC\_DABC\_D$

Breaking it down: Let's divide the sequence in groups of 5:

We can see a repeation of string of 'ABCD' with doubling one alphabet in each string starting A in first string, B in second string, C in third string and D is fourth string.

Complete Sequence: $mathit{AABCDABBCDABCCDABCDD}$

Thus, the missing letters are A, A, C, D.