What do you mean "if two consecutive records have an equal readings". The code takes into consideration if two fields have same values the n sort it via score.

#!/tools/bin/perl

use strict;
use warnings;
use Data::Dumper;

open DATA, "file1" or die $!;
my %recordsArray;
my $header = <DATA>;     #capture the header line
my @headers = split(/\t+/,$header);
while(my $line = <DATA>){
    chomp($line);
    my @records = split(/\t+/,$line);
#    print "@records";
    my $score = $records[2];
    my $value = $records[3];
    $recordsArray{$score}{$value} = $line; 
    }

print $header,"\n";
foreach my $score (reverse sort keys %recordsArray){
    foreach my $value (reverse sort keys %{$recordsArray{$score}}){
        print $recordsArray{$score}{$value},"\n";
    }
}

----DATA was modified for ids having same values-----
ID    distance    score    value    start    stop    done    remaining
+    
N_425    614    17.01    425    40    12    308    322    
N_542    1290    18.74    542    53    15    237    251    
N_372    870    15.66    372    80    15    262    276    
N_236    814    15.70    372    69    13    185    200

--------Result--------------------
ID    distance    score    value    start    stop    done    remaining
+    

N_542    1290    18.74    542    53    15    237    251    
N_425    614    17.01    425    40    12    308    322    
N_236    814    15.70    372    69    13    185    200
N_372    870    15.66    372    80    15    262    276
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