Is there any other literary technique other than metaphor in the following quote?
Solution 1:
That's about as straightforward a metaphor as they come. I detect no other figure of speech in that short phrase. Perhaps if you quoted more context something would emerge.
EDIT
Now that I see more context, the phrase taken by itself is still just a metaphor, which is part of a larger peroration (summary that concludes a speech). The metaphor may serve as a kind of metabasis (a transitional summary) that the speaker is using to persuade the audience that the aspiration that follows ("we can together strive to identify and remove the impediments ...") should be recognized and embraced. Actually, the first part of the sentence ("These, then, are our common hopes that unite us") is the literal metabasis, and the "shackles" metaphor is merely an illuminating restatement of the transitional message.