You have to finish level 1 and level 2 of first R-Type, without using powerups, using rapid fire only, and without using credits (you can lose lives). So firsts tips are: Don´t pick any powerup, don´t use any other button than "B" (Guds Skyfall has confirmed using "Y" won´t unlock the achievement either!!), and don´t die (this one is easier said than done). Now I´ll give some random tips that really made this hard achievement a little easier:
* At the beginning of the first level, try always to shoot as many red enemies as you can. They are weak, but if you let many of them live, their shots could give you trouble.
* When you see surface walking enemies, go for them. They stay on screen more time, so they will shoot at you more.
* When you see the big robot that shoot charged lasers, try to be near the ground, while its shots go above you. You´ll have to evade some shots and enemies before killing him, but he is your priority. Only stop shooting him when the blue enemy that lauches missiles appears.
* When you are next to the entrance of the base, try to be as far to the right as you can, because killing those annoying robots is your next priority. If you can kill all of them without anyone going to your left, better.
* Kill the cannons, and shoot at the missiles the blue enemy launches to you. It can be killed in a concrete pixel position from the left, but just don´t waste your time. Next kill the enemies that will fly to you, and then kill the blue enemy. Don´t waste your time going for the cannons on the top.
* Kill the circle of cannons as fast as you can, and get ready for one of the hardest parts of the level. You won´t be able to kill the cannons on the top, so try to fool them by going up and down, and kill the array of enemies that will come for you. You should go down as fast as you can too, because there are two blue enemies that could kill you. If you die, you´ll restart here without cannons or the enemies array, so it will be a lot easier.
* Now the hardest part of the level. You will have again some cannons on the top that you can´t kill, and two orange robots that takes many shots before being killed, and they will shoot many hard to avoid things to you. Focus on the first one until it´s dead. The homing missiles will not home if you are next to their feet, so try to be there constantly shooting. Once you kill the first one, the second one should be a piece of cake.
* For the boss, align to the snake´s mouth, and keep shooting. Go up when the arm´s going to hit you or when the snake shoots at you. Try to get a good timing, because you can´t miss too many shots. Once you see the four grey orbs get destroyed, aim to the snake´s eyes, you will hit some more than shooting to his mouth.
* For the second level, try not to shoot until the green enemies appears. Just avoid the other enemies, and try to be on the right side, because some of them jump earlier if you do so.
* Once you get to the part with little green enemies, focus on killing them, because some randomly home on you. Try not to shoot jumping enemies, because they will stop on the air and chances are they could kill you.
* When the green medusas come out, still focus on little green enemies, and shoot to any medusa that goes near you. One hit and they will go to the ground. Once the little green enemies stop coming, you can focus on them. If you get killed here, you´ll respawn without little green enemies or medusas, so it´ll be easier.
* When the snake comes, focus on shooting each of its parts. You should be able to reach the boss without any problem.
* For the boss, get on the little narrow space near his blue orb, and keep shooting it. Be careful about the snake´s shots, because you will have to fly up sometimes to evade them. When the snake spawns on the right, first shoot at it, and then go for the orb. When you see that you are not hitting the orb, stop pressing B, and press again a little later. That way you´ll hit it earlier than just pressing "B".
Once you manage to do all of this with one credit, this achievement will be yours. Try to practice a little before going for it (use credits, for example), and you´ll get it after many tries.
Here´s a Youtube link too, from TodaysForgotten, one of the best shmup players and one of the best Xbox forum members I´ve met in these years: