Another promising take on the "every literal life lost counts towards making the level easier" gimmick, though I found the movement to be a little too stiff and twitchy; sometimes a double jump wouldn't execute or my robot would move or jump too fast for my liking.
The grapple system sounds cool but it took me a while to figure out that my robot could only grapple onto other previous robots that I'd destroyed before. Also, it seems highly dependent on how much sideways inertia the player put in before deploying the grapple with no way to increase momentum or lengthen the grapple itself to make for a more comfortable jump.
My advice if you want to expand this (and it does seem prime for expansion) is make the overall movement speed slower and less slippery, provide less mid-air control so players are forced to commit to a jump when they make it and if you want to stick to the retro aesthetic, give the player a limited life count so they can't brute force their way through or accidentally soft-lock themselves and finally, take a look at how Bionic Commando tries its grapple system (or even Donkey Kong Country with the vines); fixed arc, fixed length and fixed swing speed allowing for precision player timing.