Brain-Flak, 160 bytes

(((((()()()()){}))[]{}{})<>()){({}[()]<<>(({})<>){(({})[()])}{}>)}{}{<>(({})<([{<({}[()]<<>({}<>)>)>()()}{}()()])>)<>{}}<>{}{({}(((((()()){}){}){}){}){}<>)<>}<> 

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Prints two trailing newlines, though one is from the interpreter.

Like Dorian's answer, this pushes 27 alphabets before processing anything. However, this solution stores it as the values 1 to 26 and adds 64 at the end.

###Explanation:

( ((((()()()()){}))[]{}{}) # Push 26 as the letter counter <>()) # Push 27 as the alphabet counter {({}[()]< # Repeat 27 times <>(({})<>) # Copy the 26 from the other stack {(({})[()])}{} # Create a descending range from 26 to 1 >)}{} { # Loop until we're out of letters <>(({}) # Save a copy of the 26 <([ { <({}[()]< # Loop 26 times 	<>({}<>) >)> ()() # Add 2 every loop }{}()()]) # Use the loop to push -(26*2+2) = -54 >) # Push the copy of 26 <>{} # Pop a letter } <>{} # Pop the 26 {({} # Reverse the stack (((((()()){}){}){}){}){} # Adding 64 to every element <>)<>}<> 

Brain-Flak, 160 bytes

(((((()()()()){}))[]{}{})<>()){({}[()]<<>(({})<>){(({})[()])}{}>)}{}{<>(({})<([{<({}[()]<<>({}<>)>)>()()}{}()()])>)<>{}}<>{}{({}(((((()()){}){}){}){}){}<>)<>}<> 

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Prints two trailing newlines, though one is from the interpreter.

Like Dorian's answer, this pushes 27 alphabets before processing anything. However, this solution stores it as the values 1 to 26 and adds 64 at the end.

Explanation:

( ((((()()()()){}))[]{}{}) # Push 26 as the letter counter <>()) # Push 27 as the alphabet counter {({}[()]< # Repeat 27 times <>(({})<>) # Copy the 26 from the other stack {(({})[()])}{} # Create a descending range from 26 to 1 >)}{} { # Loop until we're out of letters <>(({}) # Save a copy of the 26 <([ { <({}[()]< # Loop 26 times 	<>({}<>) >)> ()() # Add 2 every loop }{}()()]) # Use the loop to push -(26*2+2) = -54 >) # Push the copy of 26 <>{} # Pop a letter } <>{} # Pop the 26 {({} # Reverse the stack (((((()()){}){}){}){}){} # Adding 64 to every element <>)<>}<>