This is a story related achievement and can be gained at any difficulty.
For the fight at the end of the chapter try to deal with as many regular enemies as you can before the Handyman turns up, then avoid him while finishing off the little guys.
Skylines are your friend as always but try not to get caught on one while he is shocking it. Murder of Crows is the only Vigor than will stun a Handyman so hit him with it and then lay into him, retreat and repeat until he goes down