First, note that Ali can adopt the following strategy: He shows the cards in order until Amin picks a card. In the next step, Ali shows the largest card that has not been shown yet, and in the next step, he again starts with the smallest card that has not been shown yet and continues this process. If Amin chooses $k$ cards using this strategy, then the sum of numbers on these cards will be at most:
$$f(k) := (100 - k + 1) + (100 - k + 2) + \dots + (100 - 2k + 2)$$
We claim that for each $k$ we have $f(k) \le f(34)$. Note that $f(k) = \frac{(200-3k+3)k}{2}$ and since the minimum of this function of degree $2$ occurs at $k = \frac{f(33)}{3}$, it suffices to compare $f(33), f(34)$, and $f(33)$ is greater. Therefore, Ali can ensure that the sum of Amin's cards is at most $f(33)$. On the other hand, Amin can ensure that the sum of his cards reaches $f(33)$. Having done this, Amin never picks a card with a number less than or equal to $35$, and whenever possible, he picks cards with larger numbers. In this case, Amin can take $33$ cards such that their sum is at least $f(33)$.