Here's a basic trick for getting up and down ladders faster:

To go up, you simply press Jump and Up. You'll basically want to spam this. Although pressing Up and Jump simultaneously will work, it is somewhat inconsistent. You'll get better results if you flam them: Jump-then-Up or, more realistically, Jump-Up-Up. Unless Jason has reached the top of his arc, pressing Up a single time will not grab the ladder. Pressing it twice, however, will force a grab before he's peaked.

Going down is a bit trickier. Jason will die if he falls from a hight about two blocks higher than his own jump. He also falls very quickly, so falling down a ladder and catching yourself before dying is a real exercise in timing. Ideally, you want to fall the entire length of the ladder, catching yourself at the very last second, but this can be hard to do and even harder to practice. I recommend falling a series of shorter distances to let you build up your skill. To drop down, all you have to do is press Down and Jump. Catching yourself is easier this time around, since pressing Up at any time will get the job done. When you've reached the bottom of the ladder, or are at least close enough to fall without taking damage, perform one more drop to hit the ground. Climbing down and jumping sideways will waste time.

A good area to practice this is Planetoid C-2, the map of which is found in Dungeon-3 of Immigration Ship L-229. Dungeon-3 is found on the path to the boss Defend Them All. The pool on the second screen of the planetoid makes for a safe environment to practice falls, and the tall ladder gives you plenty of room to practice your ascent.