Where I'm from in the north, Llinos is commonly pronounced /ˈɬɪnɔs/ and in the south it's typically pronounced /ˈɬiːnɔs/ You can paste those into ipa-reader.xyz and select Gwyneth's voice at the bottom of the list to hear how the double Ll sounds in Welsh. It's not a "sh", not a "cl", not a "y", not "l." If I had to anglicise it, think of Sid from Ice Age's lisp.
None of the pronunciations here are correct because the first two 'L's in the name constitute a letter in the Welsh alphabet that's hard to convey using English phonetics. Wikipedia describes it as a "voiceless lateral fricative sound" and you'll find it at the start of a lot of place names (e.g. Llanidloes).
You can paste those into ipa-reader.xyz and select Gwyneth's voice at the bottom of the list to hear how the double Ll sounds in Welsh. It's not a "sh", not a "cl", not a "y", not "l." If I had to anglicise it, think of Sid from Ice Age's lisp.