Spoiler warning! Edit
Lethal Crisis has a total of 24 stages: 16 stages on the "Normal Route" and 8 secret stages on the "True Route". Many of the stages only consist of a single boss fight.
Until clearing stage 9 you can repeat the stages as much as you want in order to attain the objectives.
The last objectives in Stages 7 and 9 can't be fulfilled until after finishing the Normal Route. After clearing stage 9 for the first time you are locked out from the first half of the Normal Route and can only choose from Stage 10 on. You may want to create a copy of your save game before this occurs.
Clearing the remaining stages of the Normal Route unlocks the first half again so that the remaining objectives can be fulfilled.
True Route - another Spoiler warning! Edit
In order to play the 8 stages of the True Route you need to reach the "secret room" in Stage 7. To do that you require the applications "Ghost Foil" and "Spike". The former allows you to bypass the lethal gold spikes while the latter destroys the gold blocks. You also need "B-commander" to equip those two at the same time.
The stage contains a maze-like section. To find the secret room you need to follow the right directions. These directions are revealed in the "mail" section of the game manual. If you somehow make a mistake while following the path you can simply return to the first square and try again. It is recommended to neutralize the entire room before attempting to follow the directions.
Reaching the room unlocks the first True Route stage, 7B. You need to navigate the maze yet again and fight through all the enemies in the last section to fulfill the S rank objective.
You are awarded a special Custom application which you need to equip in stage 9. Beating the stage 9 boss with it locks you into the True Route - note that at this point the game forbids you from saving the game. A Game Over returns you to the title screen.
After clearing the True Route by defeating the True Final Boss every stage can be freely selected.
General Advice Edit
Finishing difficult objectives like 16S can be postponed until beating the True Route. With the higher amount of Health, Energy and powerful applications at your disposal the objectives become significantly easier.