Is there a way to implement HTTP Public Key Pinning using blacklist approach?
I mean let's say that I don't want my system/app trust in any certificate issued by root Lets Encrypt CA.
No, it's not possible to have a blacklist in HPKP. That wouldn't meaningfully improve security of a site.
the idea behind HPKP is to pin exactly one certificate (leaf, intermediate or root), to eliminate the possibility to some other malicious CA (or CA doing it by mistake) issue a certificate with your domain without your knowledge. There are few publicly known such misuse cases. Probably the most famous is DigiNotar , but there are others. See this excellent SSL/TLS time sheet by Mr. Ristic , to find them out.
I don't really understand why would you like to blacklist only one CA, because there are hundreds root and intermediate certificates trusted by browsers. Let's Encrypt is currently intermediate certificate  signed by IdenTrust root. So you would eliminate only one CA, but other hundreds would be fine? You know like worrying about grain of sand, but no worrying about desert.
Every browser has strong policy to include/exclude trust on CA in its browser. If particular CA is not in comply with the rules it gets blacklisted by browser (in case of DigiNotar for example).
I don't know if Let's Encrypt CA is just an example in your case or you would really like to blacklist this particular CA. Let's Encrypt is planning  to log every certificate into Certificate Transparency  program currently run by Google. Particular domain can be checked from logs . Currently Google in Chrome browser requires this certificate log only for EV certificates, but also DV certificates are welcome despite not being required by Chrome browser. But Let's Encrypt CA will be (is) issuing only DV certificates and all of the certificates will be (are) logged in Certificate Transparency. I have checked the community.letsencrypt.org domain  and I see it is logged fine (scroll down to the bottom of web page).
It would be interesting you explain why would you like to blacklist only one particular CA. Is this academic debate or real case use?
EDIT: It looks like Let's Encrypt is becoming root CA  in Firefox 50, that is planned to be released in November this year  and it is already trusted by Oracle Java in 8u101 version .
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