You have an inconsistent database state.
Joomla! is trying to run the instructions in
which are designed to update your database structure from 2.5.28 to 3.0.0, and it's trying to drop a column that is not there: most likely, the script was run already and didn't complete for some reason.
You might try to understand what went wrong from the log/install errors, but you'd still have to fix your database structure manually. This is very painful, takes hours, and any human error might compromise the result.
The fast and easy way: modify the script to add error tolerance.
Warning: while I have already done this previously, this is not an officially approved method and is inherently dangerous. Make a db backup first, and keep it until you have confirmed everything works as expected.
Simple as that. Edit your 3.0.0.sql file
insert IGNORE as follows:
ALTER TABLE => ALTER IGNORE TABLE
UPDATE => UPDATE IGNORE
INSERT => INSERT IGNORE
based on your current database content, you might find duplicates that are safe to delete at the end of the following tables:
#__extensions (the templates isis, protostar, beez3 may be duplicated)
#__template_styles (the styles for the templates isis, protostar, beez3 may be duplicated)
Good luck! If it fails, check the new errors you get, and comment here we might need to fix some other issues.