Some of the achievement of independent India are
1) Fully functional democracy: India is perhaps the only country which is able to avoid a strong dictator among all its colonized peer. We provided universal suffrage from day one. Indian democracy is not perfect but we regularly topple corrupt or inefficient government without bloodshed or civil war. Considering the diversity in culture and not so educated population this is a great achievement
2) Creating a country out of diversity: During Indian independence Churchill said India will soon be broken down into pieces. Many others believed the same as difference between different part of India is far greater than europe. Still we survived any major secession effort and currently very few Indian want to be a independent nation. We have 14 major languages. Two of our south asian neighbours went to civil war just because of two major language could not coexist. We have the 2nd largest population of muslim living peacefully with about a billion Hindu population without going through radicalization. In retrospect this unity in diversity will be biggest achievement of Independent India
3) Food self sufficiency: Through out British rule famine was a part and parcel of our life. Just in Bengal famine in 1943 about 3-4 million people were killed. If you consider the magnitude it can only be compared to holocaust. Even in 1950s and 60s we had literally beg USA or USSR for food grains. Currently we are completely self sufficient in terms of food which is a big achievement considering the need for feeding more than a billion mouth
5) Strong Institutions: Independent India has created very strong Institution including a fair Judiciary system, Monetary Institute(RBI, SBI), Educational Institutes (IIT,IIM,AIIMS) or research institutes(ISRO). Benefits of these institutes can be felt even in silicon valley. Also because of the achievement of students from these institutes abroad, India could create a strong software and service industry
6) Forming the base of strong economy: Because of all the above points (and many other) currently India is considered as the fastest growing major economy. Its current economic situation is somehow similar to China in 2001. As we embraced market economy 15 years after china I think it is in a comparable situation. Next 20 years of growth of above 6% can do wonders to infrastructure as we have seen in China.
People always compare India with China and come to the conclusion that it is a failed state. But in my opinion apart from China and South Korea ( I am excluding city states) India have done fairly well after independence in comparison to other colonial countries, and is poised to progress in much faster pace. My only regret is that we should have embraced market economy 20 years before. But still saying Indian government has completely failed in not entirely correct