Call of Duty's pretty easy really, providing you use all the choices and people available to you, you should have little problem advancing along and getting those achievements from the top difficulty setting.
Make sure your squad is with you:
Your squad can tackle quite a few objectives a lot more effectively than you can on your own. Use them to setup covering fire whilst you move to outflank the enemy. Make use of the available cover to stay alive and your squad will come up and take on your opposition enabling you to advance/return fire from a safer position. At the very least they'll be a decent distraction and you can get on to the next checkpoint!
Make use of your grenades:
The game hands you a limited amount of grenades but is very eager to give you a refill, so make sure you walk over downed foes and replenish your grenades to take out the next lot with.
The later 'objective' houses in Call of Duty 2 seem to spawn a near infinite amount of German's until you're able to get into them. Once you're in the house make sure you get to cover quickly (I recommend backing into a corner so you don't get shot in the back) so you can take out the germans that will inevitably come at you, your cover should allow you to stay alive long enough for your squad mates to storm the bottom of the house, although it's usually left up to you to clear the top floor! It's best to flush out the top floor with the grenades you have to get those germans moving about so you can eliminate them without too much bother.
Through the levels there's sometimes more than one route see if you can make use of these to outflank your enemy.
Sometimes it's possible to charge forward to the next checkpoint without fully eliminating your foes, this can be a quick way to advance if you'd rather get the level over with than eliminate every enemy in the area.
Don't forget about your melee attack:
Sometimes the only thing between surviving and the long slog from the last checkpoint can be the all important melee attack. Get thumping!