Does an asteroid field event affects the ‘Tactical Approach’ achievement

I've found that this can easily be picked up in the first couple of sectors.

All you really need is 50 scrap to upgrade your shield subsystem two four bars (two shield "bubbles" when fully powered). In general encounters, ignore this upgrade and leave it unpowered until you find an enemy ship that cannot get through two shields. This generally involves them having one weapon which takes a single shield off (basic laser, heavy laser, anti-ship drone) and any number of beam weapons (which are useless against shields*).

Once you've found such an enemy, it's simply a case of moving power from your Burst Laser to your second shield layer - and waiting for your Artillery Beam to destroy them.

This is probably easier to pull off early, because it's less likely that you can reliably soak all enemy damage in later sectors, even with fully-upgraded shields.

*I don't know whether enemies can have beam weapons that do more than one damage per section, and hence could penetrate a single shield, but I've not seen them. And it's safe to assume they wouldn't appear early in any case.

If you use a teleporter to send crewmen, remember as they damage a system the enemy ship loses 1hp in hull damage as well (ruining your chance for the achievement get). Same goes for systems damaged by fire spread.

Your best bet is to get 2-3 weapons that fire missiles, and don't auto-fire them. When they are all fully charged, pause, and target drone system and weapons. The drone might be able to destroy one missile, but the others should hopefully hit.