Ok I got achievement few mins ago, you must kill all planes while control big robot so problem achievement not pop for me is that use punch or shockwave on planes that might not counts so I re-do chapter and kill all planes with shooting at them instead of using punch or shockwave.
So I recommend just shooting them. Do not use punch or shockwave. That what problem with me. So best to use and keep that way of shooting. You can use shockwave or punch on other enemies while on big robot.
Lastly make sure do not use shockwave or punch on planes if plane next to or fly pass other enemies when you killing them. So watch out for it.
You can restart phase if need, just let big robot enemy punch you until you die then you go back whatever phase (1st, 2nd and last phase while on big robot) if you mistake or miss shooting at plane so restart phase you in.
My grammer might not good but I am sure you will understand and I am so much happy help you out on it.