Why Tails or Whonix? Running Bitcoin Core (which is needed for Armory) in either Tails or Whonix is a pain in the ass - the blockchain is simply too big.

I'd say the best option is to run a standalone Bitcoin Core (not managed by Armory) over Tor - you just need the Tor Browser Bundle to do that.

In Bitcoin Core: go to Preferences/Network and check "connect through SOCKS5 Proxy". Proxy IP: 127.0.0.1, Port: 9150 - and then have Tor Browser Bundle open together with Bitcoin Core.

After the above, in Armory just check check "enable settings for proxies/Tor" in Privacy Settings.