Collect 10 million bolts. This is NOT cumulative, meaning you must have 10 million bolts banked up at any one time. After defeating the Biobliterator, the game will propose that you enter 'Challenge Mode', make sure you choose to play it. You will be at the start of the game again, but you will have all the weapons, bolts, Skill Points, Titanium Bolts and Nanotech, as well as your Charge Boots, Map-o-Matic and Bolt Grabber v2 that you earned from your first playthrough.
There are a lot of changes made to Challenge Mode. Enemies are extremely strong, and you can now upgrade weapons to the level 8 Omega status. Your main concern here though is the "Bolt Multiplier". When you kill enemies in Challenge Mode, the Bolt Multiplier will go up. You can see the Bolt Multiplier in the top right corner of the screen. It will start at 1x, and the maximum it can reach is 20x. When you're hit by an enemy, the Multiplier will go back to 1x. If you can keep it at 20x you will earn huge amounts of bolts.
10 million bolts at any given time is quite a bit because you will be tempted to spend it. I recommend purchasing the Infernox armour and upgrading only 3 or so of your favourite weapons to Mega (Shield Charger and Plasma Coil especially). That should be enough for you to defeat most enemies and get through the game.
Please note that Arena challenge rewards increase tenfold too.