You seem to ask two totally different questions, judging from your image:
1) How do I get these table headers, that are not tiddlers but some field in a tiddler, into an alphabetical list
2) How do I alphabetically sort a list based on "pretty links".
...but, unless I misunderstand you, the answer may still be the same for both: I'm guessing you're using some field to define what word/s should be shown in the list.
<$list filter="[tag[B]sort[nickname]]">
<$link>
<$view field="nickname"/>
</$link>
</$list>
Yes, this assumes that you have a nickname field (...how else would you get "Bat, Huge" into the list? You've defined it after the list in your example.)
Note that the $linkwidget uses the currentTiddler as default for its "to=" argument so no need to type it out. (In fact, if it weren't for the $viewwidget you can write <$link/> to get a clickable link to the current tiddler.
<:-)