Cool mission ends in hard battle (1,2,4)
I believe the answer is:
a la mode
'cool' is the definition.
Both the definition and answer are adjectives. Maybe there's an association between them I don't understand?
'mission ends in hard battle' is the wordplay.
'mission' becomes 'alamo' (famous mission and siege from the Texas revolution).
'ends in' suggests the final letters.
The last letters of 'hard battle' are 'de'.
'alamo'+'de'='A-LA-MODE'
Can you help me to learn more?
(Other definitions for a la mode that I've seen before include "In the fashion - in France" , "all the rage" , "With ice cream on top or by the side" , "Do a meal in French style (1, 2, 4)" , "Fashionable in France" .)