Strikes are much harder than the basic levels. The first Strike, "The Devil's Lair" is marked as a level 8 mission, but even with three people, it's harder than basic level 12 missions. For earning this achievement, You can come back to a strike at any level, or complete it with a high-level friend.
"The Devil's Lair" is three tough arenas, with some minor enemies between. For the first one, You deploy your ghost to break a lock, while you fight off three waves of hive and Fallen foes, including many captains and wizards. After deploying your ghost, turn around. There's a ledge behind you. Jump up there. From the ledge, you have a good view of the battlefield. There's some cover on the left.
The second arena is a large open field with six-legged tank at the far end. Captains and other fallen will spawn regularly until the tank is dead. The tank has high health and armor, but has a weak point in its legs, especially the bright yellow line. Shoot a leg enough, and the tank's front armor will slide down, exposing its "neck." Shoot the neck for extra damage. The tank also has some very powerful forward mounted weapons. Be careful!
Ideally, the three members of your strike team should spread as far as possible. Hide when the tank faces you, and shoot the legs when it doesn't. Don't revive dead teammates, wait the 20 or 30 secs for them to self-revive. Don't forget about the fallen infantry, and this fight is easy, but time-consuming. However, the tank can easily wipe a bunched-up fire team in seconds. This can be a very frustrating fight for a poorly coordinated fireteam.
The final arena is the fight against the prime sphere. Again, Fallen infantry will spawn until the sphere is defeated. Unlike the tank fight, they are much more aggressive. The arena is laid out so it's hard to protect against both the sphere and the infantry. If you have cover from the sphere, the fallen can shoot you; but if you hide from the fallen, the sphere has a clear view to shoot you.
The best strategy I've found is to stand in the entrance way to the arena, and focus on the fallen infantry. Once there's no threat from them, shoot the sphere. However, a fallen captain will spawn immediately to the left of this area, and he can quickly charge you. I recommend saving your super moves for that guy. The prime sphere has a weak point in the center of its eye.
Keep in mind that gaining some extra levels or working with some friends makes strikes much easier.
Edit: Updates have changed other strikes quite a bit. This strike hasn't changed much yet, but please let me know if it does.