I think you're specifically referencing survival mode here. The issue with survival mode isn't that you need to get the drop on enemies, so much as it is that they are plentiful and well distributed throughout the map. It's quite easy to get surrounded in many areas of the map, where 3 or more enemies are attacking at the same time.
What you might do is practice runs around the map where you are trying not to stay in locations where you might be approached from multiple angles. Enemies tend to spawn in waves, so if you get a good run around the map going, you can kind of "train" them into a pack that will only attack from a single direction. This will allow you to more easily get to cover, since you can generally predict how the whole pack will move.
Focus on corners - you want a route that includes many corners, so that you can block their line of fire quickly. Avoid dead ends, as you'll be quickly overwhelmed if you're backed into a corner.
When it comes to the Juggernaut rounds, I try to give the Juggernauts many targets, and have body armor on. Since they move slowly, try to leave them for last, or at least for a break between enemy waves.
Having sentry guns and "sacrificial" riot team and Delta team squads can give you enough extra firepower and "meat shields" that you can take them on toe-to-toe. Flashbangs will stop them from firing long enough to generally get a clip off into them. Aim for the head.
You can also get them to try to melee you instead of firing if you get close, and then quickly back away. Their melee animation is long and can give your "backup" time to fire, but you need to ensure that you don't get hit, or you'll be in trouble.