Smack the hell out of cowrings at '@go 15'. 'Nuff said.
Before you move on, make sure you get Soul Strike for the next part (Good damage against undead, fast cast even with low dex. Needs Napalm Beat 4)
Head to pay_dun00 and smack around zombies, familiars and poporings. Boost soul strike up to lvl 10 and use that to kill everything in sight.
Head to pay_dun01 and SoulStrike Skeleton Archers and Soldier Skeletons
Head to ama_dun01 and Soul Strike Firelock Soldiers (aka Ancient Firelocks)
Either go to in_sphinx4 and use Yggsdrasil Leaves on Anubis (shift+click them) if you have the money, or you can head to gl_sew03 and Fire Wall/Firebolt Stings until reborn (bring lots of flywings or a creamy card to avoid Gargoyles).
Saplings atyggdrasil01 or Ice Titans at ice_dun03 (bring flywings/creamy card). When killing saplings, get Fireball 10 and run around in circles fireballing saplings to group them up. When they are close together in packs, you can fireball them all into oblivion. Ice Titans can be killed easily with Lightning Bolt lvl 10. They are slow and fairly easy to kill - just remember to dodge those gazettis.
Youhave two choices,
Salamanders are the prime target here. Flywing/Teleport around till you find a lone salamander. Use Spider Web to lock them in place. Wait a second or two until they fireball you (they will ALWAYS do this) then let lose with cold bolt. It helps to have a siroma card and a good rod first. After cold bolting, run back a bit, web, and repeat. Later on, you may not even needto web first before they die. Double bolted cold bolt can hit for over 45k near max int.
Again, bring tons of flywings or a creamy card. You should focus on Seyrens, Harwords, or Eremes, since they have huge elemental weaknesses (meaning super strong bolts) or they have very little MDEF (or both). Don't bother with wizzies or priests or snipers, they are too dangerous and/or tooresistant to your bolts. If you need to escape from Katrinns (the wizards) throw down a safety wall (you can tank monster magic with safety wall as long as they're less than 3 cells away from you) and try to stone curse (may be difficult due to high mdef). Use cold bolt on Seyren or Eremes, and Lightning Bolt on Harwords. You can spider web them first to make sure they stay still.
Before Ibegin, I must say that equips are extremely important on a professor. You have amazing defensive skills but you are not invincible, and having good equips will ensure you can still use your strong offensive skills.
Cards: Gibbet (5 extra MDEF), Giant Hornet/Giearth/Leaf Cat/Leib Olmai (10% wind resist/15% earth resist/10% water resist/10% fire resist), Maya Purple (cloakers becomevisible), Marduk (silence immunity)
Valkyrie Helm  - Pick either the DEX or HP helm. After the wipe raised instant cast requirement, DEX helm is probably more important
Any slotted midgear will do the trick
Angel Wings - Great for defense. Extra neutral resistance is nice but the real bonus is the 15% Ranged Reduction. This reduction reduces misc attacks, physicalranged attacks (i.e. arrows) AND magical attacks. Best used with other equips that offer ranged reduction. Since they will add together quite nicely.
Fairy Wings - +3 DEX is extremely useful these days, plus -20% cast delay lets you spam bolts like there's no tomorrow. These wings are a popular choice for professors.
Frozen Wings - +15% MATK will send your damage through the roof. Use these if youabsolutely must kill something. Also handy if you like to combo bolts a lot, which will decrease the chance someone will survive your killer bolts.
Cards: Marc (freeze resistance), Pest (9% chance of stone cursing attacker when attacked)
Valkyrie Armor  - +1 all stats and 50% stun resistance is quite nice. If you have around 100 VIT like many profs do, 50% stun resistance will...