Using mysqldump on RDS to export a large file in TSV format
Assuming RDS with MySQL 5.6 is being used, mydumper may be a better option. The newer versions have the RDS grants limitation into account and you will get all the advantages of mydumper over mysqldump (compression, parallel execution, overall faster speed, etc).

This wouldn't provide TSV data, but by using the --chunk-filesize option you can split the data into multiple files in parallel and then process them in parallel afterwards

option:: --chunk-filesize -F Split tables into chunks of this output file size. This value is in MB