Hi tmkuzma,
unfortunately bigtop command is part of linux and not tmsh commands. So if you want to use bigtop, you need to have access to SSH CLI.
There are some other commands in TMSH that can give you the level of information (and even more details), using something like:
tmsh show ltm virtual
tmsh show ltm pool
...
in tmsh, you can execute some "linux" commands, using the run /util command, but bigtop is not part of it.
You can potentially try to use run /util bash "...", but i don't think bigtop is part of the comands that can be run like this.
HTH