Normally, beating Level 70 will make the credits roll at the game's end, not let you progress to Level 71. However, to reach Level 71, you can go to Level 5. Ram wall left of the start fives times, then shoot the wall right of the start five times. Gather the key and use the new path to find the warp panel. This will bring you to Level 71. From there, you can progress as usual to Level 75, after which you'll go to Level 61.
Begin by reaching the menu where you can opt to enter Cyberspace or the Arena. Head to the Options menu and opt to change your name. Do so and change it to "CONFIG_SYS", without the quotes. Press Start and you'll reach a debug menu where you can choose any of the 75 levels to start on, your armor, Auto-Mag count, speed, lives, and rate. Press Start and you'll then start the game under the conditions chosen.
In Level 1, approach the exit and shoot it five times to reach an alternative area where you can find warps (Levels 10, 15, 20, and 25 from right to left). There, find the extra lives pod, take the lives, and then shoot the pod three times to find a key opening up an area to the west. There, you will find warps (Levels 30, 35, and 40, going counterclockwise). Head to the Level 40 warp near the dead-end and shoot then ram the wall to its right once each. Go around to the main room and use the Armor Pod. Then touch and shoot it, then take the key to open up another part of the area to the south.There, you'll find warps (Levels 40, 45, 50, and 55, going counterclockwise). Go around the corner and ram the wall to the right of the Level 55 warp once. Go around the corner to the southernmost item pod, which did not disappear if emptied. Shoot it for a key to open an area to the east.There, feel free to peruse the nearby items pods - there are warps to Levels 60 (west) and 65 (east) nearby. On the east wall, you'll notice four panels. Ram the second from the northernmost one five times, then shoot it one time. Take down the enemies that appear and you'll find a room on the other side of the revealed corridor. In its southwest corner, you'll find a warp to Level 71.
When you reach the flashing wall in the first level, shoot it five times. Turn around, and you'll see a new hallway has opened up. Down it are five exits that lead to different levels, and a pod that contains nine extra lives.
Change your name in the options menu for the prescribed effects.