No jumping. As much as I enjoy the arcade game I go by the Robo-shouldn't-jump rule (which the CPC and Spec versions went by... but then both blew it a bit with the sequel game having jumping aaaand bottomless pits... argh!) and yeah regular shots do little to no damage to him and he's not particularly fast (but not slow enough to the point of absolute tedium) and he turns round (as I do in all my game projects cos I just like doing the front and back views too for a more solid '3D' feel for the character) rather than flipping. Things like grenades and heavier firepower (cobra assault gun) will do much more damage though if it's a solid projectile it can be deflected with a punch or shot depending on what they are. I wanted him to feel like a tank as you say. Want to feel that sense he is tough and scary to the enemies but obviously there still has to be a challenge as such and carelessness will get him damaged. Don't worry. I'm a big fan of original Robo (if you saw my action figure collection of him you'd know that, heh) and keen that even though this is very 8-bit I still want it to feel like that's him there.
Here's an crappy old video (I say video but it was really screen captured gifs converted to video) I did back in January after coding his basic movement. Much of the graphics have changed in various ways since (for example in the tiles but also Robo's head is a bit smaller in this video and I made it bigger cos of the human characters and his own helmet-less head sprite and he's also missing his regular standing leg sprite, using simply the first frame of the walk cycle) but it still shows how he moves and turns and shoots. Ignore that the enemies are an old sprite sliding across. Simply to test his bullet and fist collision. Also sorry no sound in the video but he does make a stomp sound when he's walking timed with each frame where he puts a foot down.
Since then I've been adding a couple of things the old games didn't do. For example grabbing an enemy is possible (though a bit buggy at moment) lifting them up off their feet by their throat to interrogate or throw them (similar to how he apprehends Boddicker in the first film by reading him his rights while throwing him through glass). Also going in and out of doorways is possible in my game (as there's a lil bit of exploration and finding 'evidence icons'). Some doors need breaking down with a small quick 'mini-game' that occurs in the status panel bit where the gun is (replaced with a fist when punching) and this is inspired by the bit in the first film when he smashes that door down into the drugs warehouse place (shortly before the Boddicker scene I mentioned). Nothing spectacular but just little bits that add a bit more to the typical walk n' shoot gameplay. Basically anything that I can quickly code in that doesn't require much more graphics than is already available and adds more to the Robo feel of it is what I'm trying to cram in.
Recently had someone create a shader for me in Game Maker Studio so I could finally have control over colours so I can do fade to blacks using only the colours in my CPC palette which is nice and also for palette swapped enemies (even Robo has some optional colours.. the grey of his Robo 1 look can be switched to a more blue tone for a Robo 2 inspired look and a couple of other ones that may or may not stay).
Think I'm just babbling now.