mySQL running on 100% CPU both on RDS and EC2

How do we troubleshoot an issue with Amazon wherein my database queries (PHP/MySQL) are eating 100% CPU most of the day?

Traffic=200 connections average mySQL version = 5.5.40

The following specific query seems to be the culprit with each query being sorted. (Most of the time, the status is Sorting Result).

SELECT reports . * , domains.name AS dom_name, publisher.pub_name FROM reports, domains, publisher WHERE reports.domain_id = domains.dom_id AND publisher.pub_id = reports.pub_id AND reports.rep_type = 'N' AND reports.pub_id IN ( 3 ) AND reports.rep_status = 'Y' ORDER BY reports.rep_pub_date DESC LIMIT 1200 , 100

The database contains roughly 100 tables, and the biggest table is reports with roughly 3 GB size and 2,45,00 rows.

Based on the developers demands, we downgraded from being on MySQL 5.6 on RDS to mySQL 5.5 on EC2, situation remains the same. (4 CPU/15 GB RAM)

How do we troubleshoot the issue? Is it related to queries or is it inherently slow on EC2 and thereby we need to upgrade the hardware?