Yari Samurai and their double time ability do wonders against archers.
Otherwise, use a heavy armored infantry. Naginata samurai do well under sustained fire, even in close formation.
Loose formation is even better.
The best way is to not attack piecemeal. Go as one force, or in waves. Since about turn 80 I've been using this tactic to great effect.
1. Charge their line with yari ashigaru in loose formation. This has two uses:
A) It focuses their fire on your 'expendable' troops.
B) It distracts the archers, and sets it up for:
2. A charge by Yari Samurai. Using their double time charge helps close the gap faster, and stops shooting casualties. You may want to keep them in loose formation until they are close to charge range.
3. Have the flanks held by Naginata Samurai. Their heavy armor and high defense mean they can handle most anything barring the entire army.
This is backed up by a healthy dose of Ashigaru Archers. I tend to save my Bow Samurai for castle defense, where their accuracy and reload speed are paramount.
Of course, this doesn't work for every situation, but its working alright for me so far.
Hope this helps man.