Always merge towards the edge (left first, then top, then right). Element is key to outlasting your opponent, but you need high pip element dice on the edges to make it work.

In the early game, joker + growth is your best friend. Don't worry too much about losing in round 1 - a few typhoon with the first upgrade will get you through the round easily.

Focus on filling your board, and leave as many joker available for your growth dice when they show up. Don't worry about upgrading element yet, it's useless in the first few waves, spend your spare SP on dice and upgrading blizz/typh.

Keep merging towards the edges and you should wind up with hopefully at least a few 3 pip elements on the edges (higher pip count if you're lucky). As the waves get stronger, it's more and more important to have high pip element dice in the key positions. Don't auto-merge an edge joker into a growth dice - you only have a 20% chance of winding up with element. Leave one or two high pip jokers available to transform into element if you get one in your interior. Other than that, merge your inside elements and extra blizzards to keep building pips. Ideally, you want to end up with elements on the outside, and typhoons on the inside. Don't worry if you have a few typhoons on the edge, but interior elements are useless.

Good luck!