Mounting a time-limited rescue mission for kerbal inbound to Kerbin
Solution 1:
Its doable. This is what you usually do for the asteroid redirection missions.
Make a maneuver node at the Periapsis that would bring her into an Orbit. The dV for this node is a guideline for the dV of the rescue craft. This craft will have to accelerate and then again brake by at least this amount to get back into orbit and of course some spare for maneuvering.
Get a craft into orbit, that has enough dV and an orbit with the same direction as your incoming craft. Match the inclination to that of the incoming vessel.
Some-when around day 76/77 start planing an intercept at the Periapsis of the incoming craft. You might have to lower/raise your rescuers orbit a bit to get this working.
Do the intercept and as the two craft approach each other use the target mode of the NavBall to accelerate the rescuer to the speed of the other craft.
From there on its a normal rendezvous. As soon as you are close enough EVA the Kerbal over and brake into an Orbit (Don't forget you science).
Additional thoughts:
you could just send some fuel to the returning vessel, but this requires docking.
if you dock and want to bring both vessels back you will need additional fuel/dV on the rescuer as you have to move a heavier load.
you can do the intercept earlier. This might be easier as the ships move slower further away from Kerbin (giving an easier intercept), but this will again need additional dV.
Solution 2:
Although it looks like your kerbal is already lost in space. I would have recommended a Munar-assisted orbital insertion:
- As far out as possible create a maneuver node and tweak until you can get a Mun intercept.
- Tweak the maneuver node to kill as much of your velocity as possible without crashing you into Kerbin - If you have enough delta-v (300 should be heaps) this should be relatively easy.
- This will put you into Kerbin orbit so a simple docking should be possible.