8 of 15
Added result with string result as well

Java 154 bytes##

Without using String (154 bytes)

public static void main(String[] args) {
    for(int i = 0 ,k=1; i>-1; i+=k==1?1:-1){
        for(int c= 65, d = 1; c>64;c+=d==1?1:-1){
            d = d>-1 && c < 65+i?1:-1;
            System.out.print((char)c+(c+d<65?"\n":""));
        }
        k = k>-1 && i < 25?1:-1;
    }
}

Codegolfed

for(int i=0,k=1;i>-1;i+=k==1?1:-1){for(int c=65,d=1;c>64;c+=d==1?1:-1){d=d>-1&&c<65+i?1:-1;System.out.print((char)c+(c+d<65?"\n":""));}k=k>-1&&i<25?1:-1;}

With String(175 bytes)

String a="abcdefghijklmnopqrstuvwxyz";
for(int i = 1 ,k=1; i>0; i+=k==1?1:-1){
    System.out.println(a.substring(0,i)+new StringBuilder(a).reverse().substring(27-i));
    k = k>-1 && i < 26?1:-1;
}

Codegolfed

String a="abcdefghijklmnopqrstuvwxyz";for(int i=1,k=1;i>0;i+=k==1?1:-1){System.out.println(a.substring(0,i)+new StringBuilder(a).reverse().substring(27-i));k=k>-1&&i<26?1:-1;}

Thanks to manatwork