Zed is one of the only dangerous enemies. Hard mulligan for removal and similar. You should buy removal from shops if your deck doesn’t have any. Pick a support champion from a region with good removal cards even if you don’t care about the champion itself - this influences the cards you see in the shop and reinforcements.
Most encounters you can ignore what they’re doing and roll over them by building a scary board but Zed is faster and scarier in almost all cases here. You need to draft accordingly and mulligan accordingly to protect yourself against him and win after he runs out of gas. It’s quite doable if you plan ahead, and since “one or two big scary guys”is the theme of the adventure in general until asol you can take answers for such situations comfortably.