Hello,
Before reading this guide, I suggesting watching through the one minute guide for all 3 phases beginning here: https://www.youtube.com/watch?v=9bRfes93E4E
This is just so you can visually see the mechanics for the raid.

Equipment:

This is what my setup looks like in a solo run. Just a bit cheap because my account is an iron man and I haven't unlocked better gear. I prefer running thralls over venge as it does more consistent damage over time. You can camp the insulated boots the entire raid and open up another slot for food if you want to. Realistically you don't actually need a spec weapon. In fact, I suggest you not to have a spec weapon if you are beginning to learn because it may cause you to mess up your clicks. The primary weapon for this guide will be a 4 tick weapon (whip, blade of saeldor, ghrazi rapier, etc.). I highly suggest having a blood fury if you can. It will save a lot of food and could allow you to stay combat boosted longer throughout the fight.

Phase 1:
Pretty straightforward. Pray mage for safety net in case you mess up. If you do not pray mage, Verzik's attack can one hit your entire hp.
As soon as Verzik spawns, you will have time to attack 3 times assuming you are using a 4 tick weapon. This applies to the staff as well. So start off by specing twice with the staff and then switch to your primary weapon and attack again. As soon as your 3rd attack finishes, run to a safe tile behind the towers.

The tile circled in red baits Verzik to attack the middle tower. The tile circled in blue is a safe spot where you can attack with the staff.
Verzik's attack pattern allows for 2 attacks before you need to run to a safe tile to avoid damage. So your attack pattern should be attack Verzik twice and run to safe spot. You can attack again after Verzik attacks. Be careful with the timing here. If you attack too early, Verzik's attack will target you over the tower. Just rinse and repeat until you clear p1.

Phase 2:
This is phase that people have a hard time with. If you don't have insulated boots equipped, make sure they are on otherwise the electric ball will do a lot more damage. Keep pray mage on.
The attack pattern for this phase is to attack Verzik from one tile away, then step back to another tile that is different from the one you attacked from. The tile you end up on also has to be 1 tile away from Verzik. This will help in dodging the cabbage bombs throughout the fight.
The tricky part of this is that you have follow a tick pattern otherwise Verzik will knock you back and stun you. This could be fatal if you are low on hp as Verzik has time to attack with a cabbage bomb in the duration of the stun.
The best way I have found to follow a consistent tick pattern is to attack Verzik the same tick that he attacks you. You will be using this attack pattern for the entirety of phase 2.
During the course of the phase, Verzik will spawn spiders. The purple spider will heal him for a small amount until it is killed. When you kill the purple spider, Verzik will take around 70 damage. You will need a poison weapon to one hit the purple spider (abyssal tentacle, rune knife p++, blowpipe, etc.). Be careful where you are attacking the spider from. If you are attacking the spider within a tile of the boss, you will need to do it in a way that follows the tick pattern mentioned before. If you attack at a wrong time, Verzik will knock you back and stun you. The safest way is to step away from Verzik and attack the spider. Then find the timing again to start attacking Verzik again.
An important thing to remember is not to greed for hits. Make sure you are attacking the same tick that Verzik attacks. While you are finding the timing to attack again, make sure you are moving a tile per tick to dodge the cabbage bombs.
When Verzik spawns the purple spider, he may also spawn a green or white spider. These two spiders are deadly and can take a good chunk of your health if you are within 2 tiles of them when they explode. The priority is to kite the spiders when the run to you. Wait for them to walk to you until they are 1 tile away and then run away. If both the purple and white/green spiders spawn at the same time, I would prioritize dealing with the white/green spiders first before trying to kill the purple. As you get more experienced, you may choose to do the one that is closest to you.
At 35% hp, Verzik will spawn a red spider. When the red spiders spawn, stop attacking Verzik and move over to the red spider and attack it twice. Otherwise any damage you do to Verzik will heal him. Think of the red spider as Verzik gaining 100 health especially if you are doing the raid on task. It may seem awkward leaving the red spider at high hp, but I promise you it is better and more efficient to move on to Verzic after hitting the red spider twice. You do not benefit from slayer helm bonuses when attacking the red spider so the best way to make use of your hits is to attack the red spider twice then go back to following the attack patterns for Verzik. After the red spider explodes on its own, stop attacking Verzik and move back to where the red spider spawned. The red spider will spawn again and this cycle continues for the rest of the phase. Attack the spider twice and go back to attacking Verzic. Purple and white/green spiders will still spawn during all of this. The timing to kill the purple spider during this important. You have to kill the purple spider only after you have attacked the red spider twice. Otherwise, instead of taking 70 damage, Verzik will heal for 70 instead.

Phase 3:
I find this phase a lot easier than phase 2.
When phase 3 starts, pray melee and keep it on for the entire rest of the raid. You will not need insulated boots anymore so if you brought prims you can put them back on.
Verzik will still spawn white/green spiders during this phase so be wary for when they spawn.
You can keep attacking Verzik until he starts shooting his webs. When he shoots his webs, attack him once and move one tile either clockwise or counterclockwise. Keep following this attack pattern while kiting Verzik around his character model. Do not stay on the webs. Otherwise, you will be stuck to the ground and will take a good chunk of damage after some time.
After the webs, position yourself in the middle of the arena. You want to be in the middle so that you can visually see where the safe spot for poison missile is. If you are too far right or too far left, you might not be able to see the safe spot. The safe spot looks like a small yellow pool on the ground. After this, make sure you keep your hp high. After a couple of attacks, Verzik will do a guaranteed 74 damage. If you brought vengeance, you can cast vengeance before the 74 bomb hits you. After this attack, Verzik will reset his attack cycle. Keep attacking Verzik until he is around 25% health. After Verzik is taken below 20%, he will spawn a tornado that slowly walks up to you. If you stand on the tornado, you will take a lot of damage and Verzic will heal a lot. You will want to keep him at 25% health until he completes his attack that you can safespot with the yellow pool. This is the most safest way to complete the raid because if you take Verzik below 20% too soon, you will have to maneuver a lot more during his webs and missile attack. When the tornados do spawn, many people choose to run circles around Verzik. This is completely unnecessary as you can just run in a straight line back and forth through the tornado.

If you've read this far, I hope that any of this can help your solo tob runs. Just a few tips and tricks I picked up.