Not an easy thing to do.
Is the colony aggressive?
This is a question that should be asked first. In over 50 years of beekeeping and handling many more colonies than the average beekeeper handles, the number I have had to retreat from because they are too vicious to handle can be counted on two hands. I only wear a simple ring veil and no gloves, so I certainly know when a colony is aggressive.
I have been called out by beekeepers because their bees are "aggressive", but I very often find that when I handle them they are fine, although sometimes perhaps a bit "touchy". In my experience bad handling and poor use of smoke is a major reason for aggression in bees. Bees have evolved with a defence mechanism to repel creatures that break into their nest and in my view they have a right to use it if they are mistreated. Very often the bees get the blame for being aggressive when they have had a lot of help! Having said that, there are colonies that are permanently bad tempered and if so, they shouldn't be tolerated by beekeepers.
Is the colony a nuisance?
If the beekeeper, their family or neighbours are being stung, then it is clearly a nuisance and something needs to be done quickly. The obvious thing to do is to requeen it if possible, but to look for the queen will probably take longer in a bad tempered colony, so aggravating the situation.
If the colony is situated away from human activity, then it can probably be dealt with where it is. If it's not reasonably possible to requeen the colony in situ, close it up when the bees aren't flying, then move it more than 3 miles away, preferably away from habitation or where there are likely to be people close by, such as near a public footpath.
What can you do?
Firstly I must say that it appals me to hear of beekeepers killing colonies, simply because they are unable to deal with them. This in my view is a defeatist attitude that sends the wrong message to members of the public, when they constantly hear about the decline of bees.
I have heard one "beekeeper" boast that he regularly "petrols" a couple of colonies each year because they are aggressive. I suspect it has far more to do with the standard of beekeeping than anything else. I have certainly never had to think of it.
A bad tempered colony is more likely to reject a queen than a good tempered one, so I would try to introduce a poor queen that is on your list to cull, but heads a good tempered colony. If you lose her it doesn't matter much. If you haven't got one, then ask other beekeepers. During the summer you should find an unwanted queen in most BKAs. If introduction is successful, then once that queen has settled she herself can be replaced.
It is often thought that you have to wait several weeks for the "bad tempered" bees from a queen to die off before the "good tempered" bees take over the colony. I have seen estimates from 6-10 weeks, but this is not my experience. I have done the experiment several times, where I have exchanged queens from good and bad tempered colonies. In most cases the temper follows the queen and within a couple of days the colony changes character.
If it is possible to inspect the colony, even when fully "booted and suited" try to look for the queen. You will probably need to use more smoke than usual, which may drive the queen into an area where you don't expect her to be. Even though it may be uncomfortable, persevere if you can.
If the colony is so vicious it is impossible to inspect it, then you need to bleed off the flying bees, as it is largely them that will sting you. Wait for a good flying day, as it is then when you will quickly lose the vast majority of the flying bees. I have observed that not all flying bees fly on cool days.
In the morning, heavily smoke the entrance of the offending hive and move it several feet away. If you are short of space then face the entrance in a different direction. On the original stand place a nucleus or small colony, preferably in a full brood box, but it doesn't matter. This can be an existing one or one that has just been made up. If there is a queen, then cage her to prevent her being overwhelmed by the sudden influx of flying bees. If there is no queen, then use one that is on your list to cull.
The aggressive colony should lose the vast majority of flying bees by the afternoon, so activity at the entrance will be much reduced.
There should be mainly young bees left that are less aggressive, therefore easier to inspect and more likely to accept a new queen. Remove any supers, inspect the colony and look for the queen. When you find her remove and kill her. Don't be tempted to keep her! Place your new caged queen in the colony and close up. Inspect 48 hours later and release the queen.
If the colony is still so difficult to handle that you can't find the queen, then split it into two or three nucs, with any supers left on one part. Leave them a couple of hours, by which time they should tell you which part the queen is in. It is much easier to deal with a small colony than a large one. Once the queen has been found the combs can be replaced and a caged queen given.
If you are unable to do any of the above there is something else I have been reasonably successful with on several occasions. It is a trick an old beekeeper showed me a long time ago. If the colony is so vicious they won't let you find the queen, then remove the supers and place a protected queen cell between the frames, close up and leave for 3 weeks. In most cases the bees will supersede the old queen with your introduced one.