my @list = ( qw( apple Alpha aLBAtross aLbAcOre etc... ) );

# Convert our list into the ( [APPLE apple], ... ) form with map:
@result = map { [ uc($_), $_ ] } @list;

# Now sort the list:
@result = sort {$a->[0] cmp $b->[0]} @result;

# Now convert the resulting list back into (aLbAcOrE aLBAtross...) format:
@result = map { $_->[1] } @result;