Building on @Verglas's answer...
The way you'd normally do something like this in HTML is via floating.  Something like this::
<div><p style='float: left;'>Left</p><p style='float: right;'>Right</p><div style='clear: both;'></div></div>
It would be great if you could transform this into a NSAttributedString and have it work:
NSString* html = @"<div><p style='float: left;'>Left</p><p style='float: right;'>Right</p><div style='clear: both;'></div></div>";
NSData* d = [html dataUsingEncoding: NSUTF8StringEncoding];
NSAttributedString* as = [[NSMutableAttributedString alloc] initWithData: d
                                               options: @{
                                                          NSDocumentTypeDocumentAttribute: NSHTMLTextDocumentType,
                                                          NSCharacterEncodingDocumentAttribute : @(NSUTF8StringEncoding)
                                                          }
                                    documentAttributes: nil
                                                 error: nil];
Sadly, it does not work.
For a second attempt, we can try using a HTML table:
html = @"<table style='width:100%'><tr><td>Left</td><td style='text-align:right;'>Right</td></tr></table>";
Curiously, this works as intended.  What's even more curious are the attributes it generates:
2014-08-27 14:27:31.443 testParagraphStyles[2095:60b] range: {0, 5} attributes: {
     NSParagraphStyle = "Alignment 4, LineSpacing 0, ParagraphSpacing 0, ParagraphSpacingBefore 0, HeadIndent 0, TailIndent 0, FirstLineHeadIndent 0, LineHeight 0/0, LineHeightMultiple 0, LineBreakMode 0, Tabs (\n), DefaultTabInterval 36, Blocks (\n    \"<NSTextTableBlock: 0x8d9c920>\"\n), Lists (null), BaseWritingDirection 0, HyphenationFactor 0, TighteningFactor 0, HeaderLevel 0";
2014-08-27 14:27:31.444 testParagraphStyles[2095:60b] range: {5, 6} attributes: {
    NSParagraphStyle = "Alignment 2, LineSpacing 0, ParagraphSpacing 0, ParagraphSpacingBefore 0, HeadIndent 0, TailIndent 0, FirstLineHeadIndent 0, LineHeight 0/0, LineHeightMultiple 0, LineBreakMode 0, Tabs (\n), DefaultTabInterval 36, Blocks (\n    \"<NSTextTableBlock: 0x8da1550>\"\n), Lists (null), BaseWritingDirection 0, HyphenationFactor 0, TighteningFactor 0, HeaderLevel 0";
}
Scroll to the right and notice the reference to NSTextTableBlock.  NSTextTable isn't a public API on iOS, but NSAttributedString initWithData:options:documentAttributes:error: used it to generate our attributed string from HTML.  This is painful because it means we can't construct a NSAttributedString by hand (we must generate it fro HTML using this API).
Building attributed strings from HTML is slow and largely undocumented.  I avoid it whenever I can.