I'm using this regular expression
MySQL version 5.1.73
Assuming you want to test column
val then try the following:
... WHERE (val REGEXP '^[0-9a-z]*$') +(val REGEXP '[a-z].*[a-z]') +(val REGEXP '[0-9].*[0-9]')=3
This combination will test
val to be made up of only numbers and characters (first regexp), contain at least two letters' (second regexp) and at least two numbers (third regexp).