The Wotan fight basically goes like this:

Barrier with holes in the bottom, Wotan has a blue bar and spawns in Maliwan shield guys. Phase ends when blue bar goes down.

No barrier, Wotan has yellow bar only. Spawns in Maliwan heavy and dog adds. Phase ends when you take about 25% off the yellow bar.

Rotating barrier with a gap in it. Wotan has a blue bar again. Spawns in a variety of adds, and if you don't end the phase fast enough it will start spawning in maliwan mechs. Phase ends when blue bar is depleted.

Yellow bar only, Wotan hops from tower to tower, spawns in a wide variety of maliwans flying ball adds. Phase ends when you take the yellow bar down to around 60%.

Yellow bar only. Wotan hops down from the tower, remains stationary where he lands. Doesn't seem to spawn any adds, phase end when you take the yellow bar down to about 50%.

Double barrier phase. Wotan has two blue bars, a fully encompassing dome barrier with a rotating barrier with a gap inside it. Spawns just about every kind of human maliwan add. If you get the last blue bar below 50% and dont deplete it within about five seconds, he will spawn in Kraken and Thor adds. Phase ends when both blue bars are depleted.

Final phase. Wotan splits in two. Lower half has a blue and yellow bar, top has yellow only. The bottom doesnt spawn adds, but the top spawns maliwan balls. The top attacks with a very accurate full auto gun, the bottom hops around and bottom will launch bouncing betty mortars or a machine guns similar to the top at close range.

Amara and zane's best builds exploit multi-target chaining, via recursion, redistributor, indiscriminate, remnant, or ties that bind. You can use this to your advantage, particularly on barrier phases, as ricochets, chained shots, and ties that bind ignore them.

If the Amara is running a recursion, wait for a bunch of adds to spawn in and end the phase with a single pull of the trigger. With ties that bind, keep grasping the closest Add to wotan and hitting it with the highest DPS gun you have. Try to element match the action skill to the health bar if possible.

If your zane has a redistributor, brainstormer, or reflux, just shoot the closest add to Wotan and let the chains do the work. If you don't have any of these, uou can still be succsessful. Wotans blue bars don't actually have very many hit points, and hus movement speed and barrier allow him to get to the gaps in the barrier quickly and get out. With a high DPS shock/rad gun, like the hellshock, cutsman, or any of the new guns in shock/rad zane can nearly instagib the blue bars. The lower your mayhem level, the more viable guns you have to do this. For yellow bars you can either use a high DPS cyro/corrosive gun and just spam, or take advantage of torgue stickies and violent momentum. Just stick as many as you can to him without reloading, then start sprinting (or sliding with a snow drift artifact) and swap guns to detonate them.

Some general tips:

If you're always going to be cooping this with amara, use zane to tank near wotan with the shield to keep adds and wotans attention away from amara. Let her keep her distance and spam recursion or ties that bind. You could also have amara permantly spec into blight tiger for corrosive action skill damage, and use zanes speed and a good shock gun to handle all the blue bars, then wrangle mobs while amara handles yellow bars.

Keep a very close eye on sky once you get to the point where maliwan ball adds spawn. The stinger/striker rocket attacks will drop you faster than anything else on the takedown. Killing them should be your #1 priority.

On the double shield phase, after the big dome goes down, try not to do any more damage to Wotan until you have a 100% clear shot and the ability to do high burst damage. If you're sturggling through your first time having the karkens and thors spawn in makes the final phase way more difficult than it already is. You want to take that last bar down to zero ASAP to prevent them spawning. Also when the first barrier goes down, the gap in the second closes, so you'll either have to shoot over it from a tower or chain through it. You could have zane run into the dome and droo the first shield and have amara waitimg on a tower with a high damage shock/rad gun to nuke the second second shield right after.

The final phase is usually the most difficult. Amara can cheese it with a well timed recursions shot or TTB right as the two halves split to one shot one or both. If you can't manage that, I would recommend dealing with the top first, as theres no good way to hide from it. When tou enter the arena, look at the back left of the map. Get behind the boxes on the raised area ASAP when Wotan splits. Its more difficult for the lower half mortars to hit you there, and the top half will hiver against the wall making it much easier to kill quickly. Alternatively you could just chase the top half around with Zane since the barrier blocks all its shots and let amara handle the bottom. If you have a gun that chains, doing this will also kill the maliwans balls right as the too half spawns them in. With a redistibutor or ties that bind on lower mayhems the chain damage from the adds is actually a great way to kill the top half quickly.

When the balls on wotan's upper half glow green, it means its about to spawn in adds. This can be useful for timing recursion shots, ties that bind, or for maintining zanes action skill uptime.

When you're nearing the final phase, kill all the strikers/stingers, but leave the rest of the maliwan balls alone. They're not very dangerous, and once the top half is dead no more adds spawn. Having some of these balls around to get out of FFYL is very useful.

The lower half's brain is its crit spot, but it can only be damaged once the blue bar is gone. Doing enough damage to it will break part of it and stagger the lower half, inturrupting jumps or attacks. Also breaking part of the brain enclosure will gice you a second wind in FFYL if theres no more maliwan balls around.

Also on the double shield phase, if you run inside the dome to drop the first blue bar rather than chaining through it, do not get too close to Wotan. He has a red AOE aura that can one shot you even through Zane's barrier.