Your party needs to contain a Thief or a Hunter.

There are four reasons for this (from most to least important).
1) Can Equp Boots (namely Deserter's Boots).
2) High Starting AGI
3) Cheap AGI AP costs
4) High Starting PRE

The purpose of this guide is to get all the green chests in Abyss (except the Amaranthine Ring) in as quick and easy manner as possible.

The origin of this guide came from a (stupid) desire to play through Solo under the Ultimate conditions (Grind, Legendary, No Saving in Dungeons).

While I came to the conclusion that being a solo character and grinding up to Nyx (if even possible) would tax even my sanity, I still wanted the Rainbow Armor (for the status immunity) for my solo run before fighting the Dark Lord (in Pandora).

When entering the Abyss make a solo party consisting of just the Thief or the Hunter.

Equip the Thief/Hunter to optimize PRE and AGI.

From here on run from all battles unless otherwise stated.

Open all the chests on the first floor until you get the 3 ice bombs and 3 holy bombs.
Note: 3 fire, ice, and holy bombs always seem to appear on the first floor.

Choose to fight a group of 3 slimes.
You will go first.
Use ice bomb.
This will kill them all.

Repeat the above two more times.

You should be level 2. Put all points into AGI.

Proceed to Level 4. (Grab the Fire Ring on the second floor if want)

Get and Equip the Burglary Ring (from the green chest).

Find a group of 5 ghouls.
You will go first.
Use holy bomb.
This will kill them all.

Repeat the above two more times.

You should now be level 5. Put all points into AGI.

Now run up to the 22nd floor (stealing green chests as you go).

On the 22nd floor find and equip the Deserter's Boots.

Now run up to the 50th floor (stealing green chests as you go).

On the 50th floor, right before the teleporter, go back to a party of four, then leave.

Special thanks go out to the creaters of the Offical Strategy Guide and to NeoDraconis and his Abyss Encounter and Helpful Hints Guide.

Between the two of those (Offical Guide's monster stat list and NeoDraconis's monsters on each level of the Abyss) I was able to know what AGI values were needed for each floor and therefor what would be the average party AGI needed to run away from all battles at each floor of the Abyss.