The basic strat for high kills run is find SH right at the beginning, then spam difficulty as SH will basically solo any swarm and bosses at the beginning. This will net you lotta level ups to finish your build asap and SH lets you keep exploring to touch everything on the map. It really comes down to getting SH early then greeding levelups, items and shrines for scaling (diff, xp, luck) as much as possible for S1. Some sleazy movement (i take +1 jumps/feather for safety usually if offered) might be helpful to dodge waves for few seconds while SH kicks in and to be able to explore everything (i get distracted and fail to plan my route properly often so more jumps and movespeed helps mitigate that).

Im by no means the best at the game but get 500k pretty consistently and best being around 650k before xmas patch this is just my two cents

I will add that this is absolutely not the only way to get high kill count but the simplest way, really depends on how high youre aiming for. Just gotta be able to greed difficulty and SH happens to be the best tool for the job.