The update notes say:
- Added 4 more achievements along the same lines as the "Medium Rare" achievement added last week
- Renamed "Medium Rare" achievement to "Medium Well"
Since they are along the same lines as the previous achievement, they mean the player should complete both the light world and the dark world of a chapter, and the sum of the best times for that chapter should be lower than some threshold. Here are the descriptions of each one:
- Rare - Spend as little time as possible in The Forest (around 320 seconds)
- Medium Rare - Spend as little time as possible in The Hospital (around 430 or 460 or 490 seconds)
- Medium - Spend as little time as possible in The Salt Factory (around 570 seconds)
- Medium Well - Spend as little time as possible in Hell (around 500 or 550 seconds)
- Well Done - Spend as little time as possible in The Rapture (around 740 seconds or more)
About the old secret achievements:
- Suffragette - Complete the light world of the Cotton Alley
- Seneca Falls - Complete the dark world of the Cotton Alley
- Well look at you! - Input the
petaphile code to play with Tofu Boy
Sources:
Note about the times for the achievements: Many people use Super Meat Boy Stats (old repo at Google Code, new repo at GitHub) program to find out how much time they have spent on each chapter. However, the reported total time is not exactly accurate because "it counts 15 secs per completed warp zone", and people posting their total times didn't mention if the warp zone time has been subtracted or not. For this reason, the times I posted above might be quite inaccurate.
Looking at that list of multiplayer achievements and based on my own personal experience online, the majority of them will be very easy to get through regular play. Here's some tips on getting some of the trickier ones.
Mastering the Art:
Earn the INCOGNITO bonus (Multiplayer).
You need to get an incognito kill. Depending on your skill level, this could be a tough one to get. To get an incognito kill, you must fill up your approach meter to the max by keeping your target within your line of sight without running up to it or otherwise making yourself noticeable. Note that you can run without reducing the meter if they are not within your line of sight.
Make the Headlines/Tactician:
Obtain 12 different Accolades (Multiplayer).
Score at least 2500 points in a session (Multiplayer).
To be successful in multiplayer, you need to always go for the quality kills. You won't necessarily win by getting the most kills, you win by getting the most points and kills only grant you 100 points. If you are more patient, you can get bonuses to earn you even more points. Being fast an efficient will get you this achievement naturally.
This could be tough getting because you will need to be quick at getting your quality kills while still fending off pursuers. I can't really help much with this, you just gotta be a machine and some other players can be very difficult to beat. Though out of all the game types, Deathmatch might be the easiest to get it in as everyone is in a confined space and there aren't (normally) any lookalikes so should be easier to find your targets.
The other achievements you should be able to naturally earn if you go after the True Templar achievement of level 20. Depending on your skill, it might take a couple of days or so of playing. You shouldn't strain yourself over this too much if you plan on playing a lot.
Best Answer
In the patch notes video for this update it was stated that an achievement is Rare if less than 10% of all players (who have started that game) have gotten it. This means an achievement can be rare, and then as more people get it, it becomes a regular achievement.
I can't find an official MS post, but this post on trueachievements.com confirms that 10% calculation.