Which key do I need to press in mission 2 of Tomb Raider 2013

Try unchecking the 'Exclusive Full Screen' option (leaving the 'full screen' option checked). This worked for me on Win7 with an ATI Radeon 7800 series.

You need to get close to this opponent so that he swings his melee weapon at you.

When this happens scramble out of the way (Shift on PC w/ keyboard, B on Xbox controller or O on the PS3), this will leave him exposed and stationary for a short period of time, now is the moment to attack the target.

After a short time he will raise the shield again, so you might have to repeat this pattern a few times (if I remember correctly this first shield guy is also wearing armour, so requires more time than others that come later).

Later in the game you can obtain other options that make shield guys easier to deal with (counter melee attack built in to a scrambling-dodge, for example), but the basic strategy is the same - get close, force them to expose them self, counter attack.