These five achievements must be earned in Matchmaking.
Earn a First Strike Medal in a Matchmaking game.
To earn a First Strike medal, you must make the first kill of the match. Invest some time in multiplayer and you'll earn this one eventually.
Win a game of Invasion in the 1st phase.
Earning this achievement requires a decent team. Just keep playing invasion (or enlist the help of some skilled friends) and you'll get this one eventually.
What's A Killing Spree?
Earn a Killing Spree in multiplayer Matchmaking.
To unlock this one, you must kill at least five players without dying. With practice, you'll be able to manage killing sprees quite often.
Knife To A Gun Fight
As an Elite, kill 5 Spartan players in Matchmaking.
In Invasion, kill five Spartans while playing as an Elite and this achievement is yours.
Be My Wingman Anytime
Let a teammate spawn on you 5 times in an Invasion Matchmaking game.
As with the other matchmaking achievements, this one will come with time. If you're playing with a friend, you can have him or her help you unlock this achievement by getting them to spawn on your exclusively.