One solution could be creating a function to be used with a forEach and evaling it (so it runs quickly). Assuming your collection is "article", you could run the following:
var runUpdate = function(){
db.article.find({"comments.user":"test").forEach( function(article) {
for(var i in article.comments){
article.comments[i].avatar = 'new_avatar.jpg';
}
db.article.save(article);
});
};
db.eval(runUpdate);