I will make here a summary of Gamewiz great Guide for solo leveling. Check it out for more information and give it alike.

If you play the enhanced Version: The Level in the Main Menu isn’t the Level for the classes. You are leveling the classes separately from scratch in each new Mission.

So the level of your Classes isn’t permanent. The longer you play a single Mission, the higher your Level gets. Considering that you are not getting a Class to level 7 in a normal MP Mission(except you are moving very, very slowly) and that there is a high chance this game will be dead someday. (The Normal Version is dead already) there is a good way of leveling all your Classes solo.

Champion of the Lions – Unlock all Assault Terminator’s abilities in multiplayer
Killing machine – Unlock all of the Heavy Weapon Support’s abilities in multiplayer
Epistolary – Unlock all of the Librarian’s capacities in multiplayer
Phoenix light – Unlock all of the Apothecary’s abilities in multiplayer
Chapter pillar – Unlock all Tactical Terminator abilities in multiplayer

Step 1: Host a Game with a password (just in case) and deactivate the Codex Rules. Select Chapter 1 and the easiest difficulty. Go to the Spot on the following Picture. It is located between the Spawn area and the Center hall with the nice big Bell. Kill all the Hybrids in the Spawn Area first before moving to the Spot:



Step 2: Now close and hack all the 4 doors as shown on the Picture and get in position.
Gamewiz has marked the positions for different Classes but basically, you go on Point C for Melee Weapons and somewhere between his Current Position and Point B for every other Class.

Kill all the filthy Xenos and switch to Apothecary if you are getting low on health. Be aware that switching classes/weapons is causing to reset the skill cooldowns and Level Ups vanishes all Cooldowns. You switch Classes and Weapons by pressing the Key “I”. Be aware that the game continues and you cant pause it. Leveling each Class takes between 40-70 minutes on that Spot. Depending on how good you clear the Spawn Area there seems to spawn more enemies but I can’t confirm this a 100%.