After AxTLS update to v2.0.0, the ESP8266 can work with TLS v1.2, the major restriction for this small device communicates with AWS IoT natively.
An in-depth walkthrough is available at https://raphberube.com/blog/2019/02/18/Making-the-ESP8266-work-with-AWS-IoT.html
First: Update ESP8266 Arduino core to last git version, Here are the instructions
http://docs.aws.amazon.com/iot/latest/developerguide/create-device-certificate.html
Converting PEM to DER format: (On Windowns you should download openssl first)
$ openssl x509 -in aaaaaaaaa-certificate.pem.crt.txt -out cert.der -outform DER
$ openssl rsa -in aaaaaaaaaa-private.pem.key -out private.der -outform DER
copy cert.der and private.der to sketch data folder and upload it to SPIFFS using arduino-esp8266fs-plugin
Some sketch examples are available in examples folder of this repository.