Can you gain achievements while in Offline Practice Mode?
Solution 1:
Besides the one training mode achievement, no, you can't.
Considering you are online, you could create an empty server for yourself and add some bots (tf_bot_add) to it (just make sure sv_cheats = 0). I've gotten a few achievements this way. Also, be sure that you're using a supported bot map, otherwise you'll need to use nav_generate.
Hope this helps.
Solution 2:
As far as I know you can only gain achievements online. Plus must of the achievements require you to be online. Really. I have all the TF2 achievements, so I know.