Yeeehaw did it solo too!
Here's some tips:
Note that to get the Millionnaire achievement you'll need to go beyond arena 9!! I died -stupidly- while getting out of arena 11, which is more than 5k meters deep, and scored 1 099k.
Also note that every arena after 9 is the same: no ennemies, the wall breaks as you step in, and red dots of death are floating all around. Just speed through (you dodged those red dots right? no? ...) and dig your way out.
The Lightning/Electric weapon is godlike in the beginning (charge it, and release to fry everything in its electric field)..
It will get you easily through the 4 first arenas. As mentioned above by Lakeshow, try to kill everything you come by to gain points.
Now for arena 5 and on, you definitely need to upgrade that pea shooter of yours. You NEED to have the 3-way attack when stepping in arena 5.
You can get through without it, but from there things will get out of hand real quick if you don't have an upgraded gun. Upgrade it, love it, never unequip it (err.. don't forget your lantern though).
: Electric Gun, 'nuff said.
: Just shoot the worms' head, not their body, and they'll be down in one go.
: Know my advice about upgrading? Well with a 4 way shooter this is a breeze.
: This one might just be a little close in timing because it's hard to kill everything (there are some shield critters that you might not get)... Shoot the "Black Hole" ennemies first (or they'll toss your lantern around... not fun!), and then try to kill everything that remains on the right side, the "Wall Monster of Doom" should get the rest on the left side and you'll have enough time to dig your way out.
: Here you just have to train and dodge those electric critters while shooting. Try to kill the enemies that are on your path before they light up, and then moving along the walls of the arena while shooting a 4-way gun at them should do it.
: This is fairly easy because the squid ennemies run away from you, and more often than not they will run into the big "Wall Monster of Doom" following you from the left and die on their own... You get the Marathon ach as soon as you step in there.
: Dodging and shoveling. Learn how to clear those rocks fast! I don't like the "Shield weapon shoveling" cause it always seems so random...
Rather, learn which rock you need to move to be able to pass through! The rocks are always the same, and even though they "fall" differently each time, it's always the same 2~ rocks that will be in your way.
Know how they look like, go straight to them, pick them up and drag them back = shoveling the other rocks on your way!
The path between the arenas is randomised, but you should be able to recognize which portion you are coming into, and what you need to do.
Know which one gives you the most trouble and try to find a way to get trough it.
Between arenas 7 and 8, 8 and 9, and on you won't have much time to think, you need to know what you're doing.
Unfortunately, some portions are almost unbeatable when you're alone and deep in the tunnels... I know that the one with 3 grabing monsters always spelled death for me if it appeared after arena 5.
Well those are my tips anyway... Hope they work for some others!
Sorry for the poor English at times
And sorry for all the names I made up for weapons and ennemies... Don't know the real ones, if there are any?