It is a hard creature to outrun due to its heavy paralysis, it is also not a good idea to run them as it's very fast and can haste (check the video at the end of the page).
Mages: This is a hard monster to solo as a mage, but if you are to kill due to the quest then try not to face it below level 80 as 2,000+ mana and the use of Great Mana Potions are recommended. Use Energy Ring so as to not worry about Magic Shield running out at the wrong moment. Unlike Giant Spiders, the widow is strong to fire so Hell's Core will hit less, just take a Wand of Voodoo or Underworld Rod and attack it with SDs while drinking plenty of Great Mana Potions. Terra Set is also recommended, although you might want to wear a Protection Amulet or SSA rather than Terra Amulet. If your level is below 60 then you will most likely die even with Magic Shield. It is possible for a level 60 mage to solo The Old Widow using Energy Walls and Sudden Death runes.
Paladins: Level 80+ can kill it by using Assassin Stars and mana shield (or Energy Ring). Just run it south of the teleport so that only the Old Widow can get close to you, and keep using Strong Mana Potions or Great Spirit Potions when your mana falls low.
Knights: Level 80+ can kill it by using Defensive Fighting. Great Health Potions and Exori Gran. Always drink Mana Potions and shoot Exori Gran with full hp. If your level is below 80 you will have high chances to die, because the Widow will deal you more damage than the one you can recover.