How can I batch a drop column operation?
I think the following thread might prove useful to you: MySQL Drop Column From Large Table

The suggestion is to copy the data to a new table MINUS the column you wish to lose, then drop the old table and rename the new one.  This is if you can't secure a maintenance window, say overnight/off-production hours, to do the work instead.

From my understanding - and others, please correct me if I'm wrong - although you could clear/NULL the data in this column in batches, you couldn't drop the column in batches since a column drop implies rewriting the row without that column - and you can't have a row in a table that doesn't have an attribute column that the other rows have.