Play campaign 1 quest 1 on narrative difficulty, pass the first section by either killing all the enemies or by resolving the objective, travel and, as soon as you skip all the quest story text and get to the board again, press
and restart the quest. All spider kills, the objective resolution, resources spent, damage dealt, etc. count for their respective cumulative achievements.
If you want to go for the objective (and advance on the Strider and Phial of Galadriel achievements at the same time) you can use a deck with Aragorn (2 willpower x 2, given that he can attack twice), Arwen (3 willpower) and Gimli (1 willpower), which adds 8 total willpower to finish the section very fast in only one turn (given that Sauron doesn’t play the “Turned Around” event which resets the objective back to 8 causing you to actually go an additional turn, but that doesn’t happen very often).
If you want to go after the spiders instead (and advance on the Executioner and Ungoliant Foe achievements among others) you should go by a deck with high damage heroes like Dwalin, Dain Ironfoot and Gimli, with a lot of damage dealers’ allies with a less than three cost like “Westfold Outrider”, character ready cards like “Ever Vigilant”, a lot of weapons, etc. Each go will net you a minimum 8 damage plus whatever Sauron throws at you until you manage to resolve the alternate “kill all enemies” objective (which I’m not sure counts towards the Strider achievement) and travel.
This method should only be used if all other achievements have being dealt with and no other way to grind travels is available (for your sanity). This is one of the very last achievements you should worry about.