Yes, you do need to obtain a Certificate of Eligibility any more to sit the QLTS assessments. The SRA has removed this requirement from March 2015.
Make sure first that you are entitled to seek admission as a solicitor of England and Wales via the QLTS. This means that you hold the correct professional qualification in a jurisdiction that the SRA recognises, and that you meet the SRA requirements as to character and suitability. You will be subject to a full check on character and suitability when you apply for admission.
This means that amongst other checks we will require a certificate of good standing from your home bar/professional/regulatory body.