Sequence 01, Memory 04 -- A Hard Ride
Once you reach the bottom of the town the Captain gets into a carriage and drives it away -- but lucky for you there is a very long rope attached to the back dragging on the ground -- hooray! We grab the rope and are dragged along behind, needing to swing from side to side to avoid rocks and things, while we pull ourselves up the rope towards the back of the carriage. But part of the way there the rope starts to separate! So we have to pull ourselves past that point as quick as we can or risk being lost.
Here is the thing -- this whole sequence is not what it appears to be -- and if you play it like it appears to want you to, you are going to get frustrated until you figure out that it is really just a scripted set of events!
First thing you need to accept: you are not going to be able to get on the back of this carriage no matter what you do, so do not get over-excited when you finally get close to it. The Captain will hijack another carriage, this one will implode, you will narrowly miss being trampled to death by a pair of horses, and then you will somehow miraculously grab the bottom of yet another carriage -- and then the scripted carriage chase begins.
The Required Carriage Chase
The second thing you need to understand: You are not actually supposed to disable his carriage. Your actual goal is to survive the many impacts with it while avoiding the rocks in the road so that you get to the place in the road where it splits -- in order to trigger a CS. That is it, that is all you have to do -- simply survive!
The way to beat this level is to NOT slam into him but move your carriage next to his and rub it, doing damage that way but be VERY careful not to drive YOUR carriage over the black parts of the road as that is rubble and will damage it. Eventually you will reach the point where a CS plays and your carriage is destroyed by a grenade-throwing Templar -- you see you were never meant to succeed here!
Once you fall down onto the rocks that ends the memory, gains you 100% synchronization, and plays the CS in which the next memory is started, with the Captain inexplicably stopping at the bottom of the road and dispatching a Templar Squad to deal with you.