Conscientious is built on conscience, KON-shuns, and came into English from French and Medieval Latin. The sci part keeps the sh sound it has in conscience. It does not sound like the sci in science.
The second sh comes from the ending. Before -ious, the letter t usually becomes sh, as in cautious, ambitious and infectious.
The ending also moves the stress. Conscience is stressed on the first syllable, but conscientious is stressed on EN, the syllable just before -tious, like am-BI-tious and de-LI-cious.
Build it in steps: kon, shee, EN, shus. Then join them, with EN the loudest.