I am not a linguist but I do enjoy reading about linguistics. I am not an expert in IPA but I have studied it somewhat. I have read the articles in Wikipedia on how to do the sounds below but I still can't produce them. I hope someone can provide some help.

1. Retroflex sounds ◌̢ (e.g., ʂ)
2. Palatalized sounds ◌ ʲ (e.g., ʃʲ = ɕ)

Mastering these would help with Japanese and Chinese pronunciation so I am extremely interested.

Alright, so here are my findings.

1. I was able to produce the retroflex, I think, imitating an Indian accent helped a lot to prepare for this. This point is not a problem anymore.

2. To me ɕ sounds somewhere in the middle between s (s) and sh (ʃ) and that's how I am producing it. However a Japanese native's opinion would be very helpful. I wouldn't mind getting technical here but I would be contented enough if someone would specifically address my intuition about ɕ lying between s and sh.

EDIT: I am still have no idea about tɕ. I am just producing a regular ch (tʃ). I wonder how bad will this affect my accent if I never correct it.

English r is a retroflex sound, so if you combine sh and r you will most likely get the ʂ you are looking for.

To me, ɕ is between she and he. In fact, the difference between Japanese hi and shi is fairly subtle.

tɕ is the same, but with a complete stop before it, just like chic becomes cheek.

I've also noticed that most of my female Japanese students tend to sound their し(ɕ) closer to s than sh, I feel this is because it sound cuter / retardish that way. Like, pronouncing susi rather that sushi.

As for tɕ it sounds more like t + ɕ to me. U_U