Hello, I want to first explain why Ivern top is actually not that bad. First of all, Ivern has a lot of tools to prevent melee characters from getting to him, namely his root and his massive e shield and slow. Which lane has the highest concentration of melee characters? Top lane. While a lot of Ivern's best synergies are with the tanky bruiser tops, you could also argue that the jungle contains more characters that Ivern would rather use his e on because of the jungle having more mobility than your average toplaner. The longer lane is a blessing and a curse at the same time. You can abuse the longer lane to have daisy run down the enemy, capitalising on your E slow, leading to more kills. Compared with mid, your enemy is less safe. Ivern has a lot of setup for his own jungler consequently, however he is also prone to being ganked. Contrary to popular belief, Ivern's duels are actually very solid, especially for a support character. Daisy is basically a toplaner by design, immobile, tanky and has cc. Using this fact, you can support daisy as an enchanter and have her solo kill a lot of targets. You are conditionally very strong if your able to keep daisy alive while not being dived yourself, meaning a lot of matchups can be polarising.

If you win level 1 into a character, which you do into most tops bar ones that have an exceptionally strong level 1 like teemo, darius, etc. you can use this strategy to get a favourable trade. One advantage of this is that unlike teemo it is much less expected, meaning you can cheese people much easier. By placing a bush as follows, you mislead opponents into thinking that you are in that bush, when you are in fact next to them. This means that they are more likely to overextended, allowing you to proc electroctute, aery or comet and chunk them with bush empowered autos.If your laner dies, or goes for a tp play you can severely punish them with your amazing tower take, much like a yorick. In this image, Kayle makes the mistake of rotating to help her jungler and dying in the process. Look how many plates I have taken in the time it takes to get back to lane.
With this big of a gold lead, her lane is functionally over. You shouldn't try and match people's tp players and just focus on taking plates, you will probably get more gold, they will miss xp and you will be able to tp back with an item advantage. If you get first tower, that's even better, more gold for your team.

Early game, you want to play passively. Your bushes are your best friends, use them to get empowered autos and auto the enemy whenever your comet/aery and manaflow are up for efficiency. You can play aggressive level 1 into certain matchups who can't actually abuse you, almost playing like a budget teemo. Level 2 you can also be fairly strong, just watch for champs who will trade you along the lane. You can play the wave two ways. In a matchup with strong early pressure, i.e. nasus, you can slow push the wave and crash it when the cannon wave comes (tip, auto the enemy and then tank the wave with E to waveclear and make your minions not take damage), allowing for a recall and to avoid any ganks. The second way to play is to play respectfully in your wave, since it is unlikely you will lose trades with E shield, minions and bush autos, especially if your running bone plating. Bait the enemy if they are stronger level 2 into hitting the wave and concede CS if necessary until you hit level 3 so you can disengage easier.

Ideally, you want to set up a scenario where you A. Crash the wave and have it slow push back so you can establish a freeze, or to conserve HP and tank the wave shoving into you with E to hold the wave in a freeze. The method depends on matchup, irelia will push with her Q for example so you can go for option 2, since she can't all in you under tower and is in a very bad position when the wave is frozen, she likely doesn't beat you without passive stacks too and can't Q you if you tether well next to your tower.

If you have suvived until level 6, well done. Your character really becomes online now, able to solo kill with the assistance of Daisy. If you have TP, you can reset and pick up some AP items, or boots for more kiting potential. You want to have the enemy push to your side of the map, so Daisy can attack for a longer period of time. If you land a q, you should use r and then have Daisy run at the enemy across the lane, keeping her alive with e. If they decide to tunnel you, all you have to do is survive while Daisy keeps ticking at their health bar, if they kill you they will surive since Daisy dies too. Lets say the enemy goes for a TP play since they are bored and think the lane is over anyways, you can waveclear with e and have you and Daisy target the tower. Not only can daisy damage and tank the tower, your bush empowered autos work against towers. This means that AP on Ivern dramatically speeds up your tower take since it is not only affecting the base damage, but the bush empowerment and Daisy. You can shred towers really fast, to the surprise of many. You can also snowball lane very well suprisingly due to your E waveclear allowing you to waveclear safely with daisy and having massively positive trades whenever you land Q and chase with Daisy.

This is exactly why matchups like Irelia and Camille are bad, they can easily force or waste your R and then play passive. They don't exactly win while your R is active, not early that is, but once its forced, you can't actually fight them alone and they can very easily force a fight.

The reason why Daisy is so strong is because of your heightened gold income and XP, Daisy scales really well with levels and AP so playing top can lead to some funny moments where Daisy can easily solo a toplaners or a bot duo if micromanaged correctly.

Despite Ivern's quotes about playing with other people and not being alone, you have an important decision to make, should you teamfight or should you splitpush. If left uncontested, Ivern can destroy towers very quickly as mentioned before, and with Daisy he can also 1v1 a ton of characters. This can draw a lot of aggro, as people usually see Ivern as a free pick since he is immobile, however the fact he is immobile means there is a lot of power put into the rest of his kit. Ivern gets really good waveclear once his E can kill casters quickly, and Daisy can help too. If you are chased, you should make a decision if you should fight or run. If you run, use your triggerseed and root to stall and make distance from your enemy. You can also tether far away from the tower if you find yourself in danger and use Daisy to splitpush, giving you a lot of safety relative to other splitpushers. Ivern is also a strong teamfighter, able to peel with his kit and tank with Daisy. Since most toplaners are pretty bad at teamfighting you should win a lot more fights with Ivern, since he just brings more to the table.

This is a hard decision to make since Ivern's teamfighting is excellent, but his ability to draw pressure is also excellent. You should consider who can match you when splitting and decide if you should be the one to split. If you have a strong mid or jungler, you can let them sidelane instead. This is a good strategy as you have an XP lead from being a toplaner, allowing your camps to be claimed almost instantly and providing buffs to your team. Main things to look out for is for assassin mid/junglers who can delete you, since Ivern likes his long trades with Daisy this can prove challenging when an assassin 1 taps you in 0.01 seconds, you can use shield to mitigate some damage but serpent's fang woud ruin your day. Highly mobile toplaners can also prove challenging, as in burst mobility not high move speed characters. Irelia and Camille come to mind. You should focus on teamfighting because these characters will not target you in a teamfight, or at least it is much harder due to Irelia's lack of a wave and Camille usually having a better target since you are fairly survivable with your shield and cc, or so she thinks. Aim to peel your carries from the two and shut them down with cc from root and Daisy. You out-teamfight these champs hard IMO so you should force them to group with their team rather than answering a splitpush.

I will add more matchup info as I play more games. I need to refine the playstyle, as I think my runes, summoner spells and items are pretty solid by now, its just the mentality behind this strategy.