Let's say I have two Muscle Slivers, so they're both 3/3 creatures. Now if they attack at the same time, and I kill one Muscle Sliver, would the remaining Muscle Sliver continue to stay at 3/3 for the attack phase, or would it instantly become a 2/2?
As soon as one of the Muscle Slivers leaves the battlefield, its ability disappears, leaving the other sliver smaller.
Static abilities on permanents create continuous effects, functioning as long as the permanent is on the battlefield, no longer and no shorter. They are not activated; they simply are. That's why they're written as statements of fact: "All Sliver creatures get +1/+1."
So for example, your opponent could block one of your 3/3 Muscle Slivers with a 3/3, and one with a 2/3. All the creatures deal damage to each other simultaneously. State-based actions are then checked, and the two 3/3s and the 2/3 have taken three damage and die. The first Muscle Sliver is now gone, so the remaining one is now a 2/2. State-based actions are checked again, and that sliver has two damage marked on it and now only has two toughness, so it dies as well.
Remember, this doesn't affect the amount of damage dealt, since all the damage was dealt at the same time, before anything died. So when you ask "does it stay at 3/3 for the attack phase?" the answer is... yes and no. It's still a 3/3 when it deals damage, yes. But it gets smaller immediately after.
The key to this one is timing and the flow of events from one game phase to the other. During the Combat Phase, there are steps of Declare Attackers, Declare Blockers, and Combat Damage.
The slivers are 3/3 creatures for as long as both of them are in play. However, damage counters remain until the Cleanup Phase at the end of the turn, after the Second Main Phase. So, during the declare attackers/declare blockers phase, they are both 3/3 creatures. Then, they are assigned the damage from their respective blockers.
If one takes 3 damage, and one takes 2 damage, it resolves like this: The sliver with 3 damage counters dies as a state-based action, resulting in the loss of its static +1/+1 global bonus to slivers. This makes the other sliver a 2/2. Since it still has 2 damage counters on it (and will, until the Cleanup Phase), it ALSO now dies as a state-based action. All of this happens AFTER damage is assigned, following the Declare Attackers/Declare Blockers Phases.
So, yes. For the attack phase, they are both 3/3 creatures, and each deal 3 damage, regardless of whether one or both of them would die as a result of that combat.
It depends how you kill it, if it is through blocking, then they'll both still be 3/3 for the damage step, but if you cast an instant, like lightening axe in the declare blockers step, the muscle sliver dies, leaving a 2/2 muscle sliver.