Yes, there's a way. I just had the same issue. Why Adobe Reader is asking for the language pack i don't know.
But i know that the best way to create multilingual PDFs is to use the Arial Unicode MS
-Font which is included in windows. That's the font with the most characters according to wikipedia!! But there's no Bold or Italics. You can buy a Arial Unicode Bold from http://www.linotype.com/en/817674/ArialUnicode-family.html#.
I use the Arial MS Unicode-Font with chinese, japanese, cyrilic. For western languages i use the normal Arial so i have italics and bold.
An other possibility is to use for each language a own font which is made for this language.
To make the Arial MS Unicode to work with tcpdf follow the steps on the answer of this Question: Creating PDFs using TCPDF that supports all languages especially CJK
I hope i could help...