Is it possible to save the optional characters without lots of speed upgrades?

I might be missing something, but even in most straightforward resques such as Battle of Mt.Dingjun i don't even get to the top of the mountain by the time the character dies.

Tried re-doing several other stages and i can't say it was any better there either, i don't even get enough time to make it to the spot, not to mention kill an enemy officer.

In case you don't know yet:

When you equip a title you get a bonus described on title description. If you increase a title past lvl 5 you can master it. Mastered titles get their equiped bonuses increased.