With some analysis tools i decided to not try and win games but try to get S/playing better which usually results on winning the game. I'm no big player, but i guess you could use some tips. Also, since there are different ways to play ivern (not too many but still...people came up with full ap ivern which is very good for buffing Daisy) i'm just going to tell you as i play him as a support jungle (as most the community do.)

As said athene's is the best item on him: mana-health regen to do camps with no problem, cdr and heal on shield so you should get it after ionian boots. After that most people take redemption, solari, etc, you could see that in guides and the recommended items.

I decided to pick targon/face of the mountain as third item (after boots/athene). It gives you another shield with slow and a good way to make money. Ivern's score suffers from low creep score and moderate gold, i felt i needed a way to steal lane creep from my teammates without hurting them too much. I gank, double shield them, then give them money from the item passive.

As forth item i try to get a zz'rot. Again i needed money and cs. This help you with some resistances and to get towers quickly. Usually with this item there's the transition to mid-late game. Redemption is a good item, to increase your heals and healing in general, but imo redemption is best when doing teamfights, face of the mountains help with the little skirmishes you have in the mid-game. In any case i get this as 5th item, trying to get rid of my boots (since i then cap cdr) 6th item would be solari/ ardent censer selling my jungle trinket. For this you have to choose for an aoe shield or a buff with attack speed champions (i'm getting it less for "adc i 2017 lul"). In any case you could sell your boots for the remaining item. This focuses really much on the shield even though it has been nerfed it is a good spell overrall. Item p.s. imo jungle item is pretty useless, you don't use warrior because your damage is mostly magical; luden echo damage isn't that impactful; ivern w makes him a ranged champion, you can't use cinderhulk effectively; similar with bloodrazor, you don't have a kit to make good use of onhit effects; and you want to use smite to instantly clear themp.

For the gameplay: I play very aggressively with an "hit and run" style trying to counterjungle as much as i can when i have smite available and trying to stay as much as possible far from the enemy jungler. I read somewhere that 2v2 with ivern are powerful but meta jungler like lee, vi, hecarim, nocturne, evelynn, rengar, kha can stomp you and your teammate if they have someone who can support them. Once you have daisy this can be much easier but still, there's the risk of an outplay. Once i became confident on ivern i started to use exhaust/smite as my summoner spells. I mostly don't nerd flashes to make plays or use insane ultimates (spell aren't so "bursty" impactful so..) and q + red plants can get you through the jungle fast. I should've covered all. Lastly: don't forget to ward/pink ward, that's obvious but help with scores and visibility